Quant :quiz

Quant :quiz

1.Ram starts working on a job and works on it for 12 days and completes 40% of the work. To help him complete the work, he employs Ravi and together they work for another 12 days and the work gets completed. How much more efficient is Ram than Ravi?

A.50%

B.200%

C.125%

D.100%

2.Two taps can fill a tank in 12 min and 18 min respectively. Both the taps are kept open for 2 min and then the tap that fills the tank in 12 min is turned off. In how many more minutes will the tank be filled?

A.9

B.12

C.13

D.10

3.Pankaj can produce one unit in 15 days, while Bharti can do the same in 12 days. After producing one unit, working together, they received Rs. 90, which they distributed amongst themselves in proportional to their efficiency. If they work for 20 days, and sell the produce, then Bharti should receive

A.Rs. 120

B.Rs. 140

C.Rs. 150

D.Rs. 160

4.Pavan builds an overhead tank in his house, which has three taps attached to it. While the first tap can fill the tank in 12 hours, the second one takes one and a half times more than the first one to fill it completely. A third tap is attached to the tank which empties it in 36 hours. Now one day, in order to fill the tank, Pavan opens the first tap and after two hours opens the second tap as well. However, at the end of the sixth hour, he realizes that the third tap has been kept open right from the beginning and promptly closes it. What will be the total time required to fill the tank?

A.8 hours 48 minutes

B.9 hours 12 minutes

C.9 hours 36 minutes

D.8 hours 30 minutes

5. 40% of the employees in a factory are workers. All the remaining employees are executives. The annual income of each worker is Rs. 390. The annual income of each executive is Rs. 420. What is the average annual income of all the employees in the factory together?

A.390

B.405

C.408

D.415

6.In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?

A.2

B.2.5

C.3

D.3.5

7.A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?

A.17

B.23

C.77

D.None of these

8.When processing flower-nectar into honeybees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 15% water?

A.1.5 kgs

B.1.7 kgs

C.3.33 kgs

D.None of these

9.Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?

A.Rs. 15

B.Rs. 15.70

C.Rs. 19.70

D.Rs. 20

10.If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?

A.25%

B.16.67%

C.20%

D.33.33%

Answers 

1. D

2. C3. C4. B5. C6. C7. B8. (B)Flower-nectar contains 50% of non-water part. In honey this non-water part constitutes 85% (100-15).
Therefore amount of flower-nectar needed = .85/.5*1= 1.7 kgs
9.(C)
Let the amount taxable purchases be Rs. x.
Then, 6% of x=30/100
Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70
10. C

Therefore 0.5 X Amount of flower-nectar = 0.85 X Amount of honey = 0.85 X 1 kg
x=30/100*100/6 = 5

Quant Quiz

Quant Quiz 

1.    If separate teams of four or six or eleven students are made from the students of a class, three students are left in each case. The smallest possible number of students in the class is

(1) 132
(2) 135 
(3) 136
(4) 138

2.    The S.I. is 7200 on 12 p.c.p.a. for 6 years on a sum. what is C.I. on 5 p.c.p.a. for 2 years

(1) 1020    

(2) 1055    

(3) 1050    

(4) 1025  
  

3.    Find the approximate average of the following set of scores

1566,  2455, 1231, 2678, 1989, 3342, 2715

(1) 2590 
(2) 2555 
(3) 2268
(4) 2282  

4.    The population of a city is 1500000. It increases by 10% during 1st yr, decreases by 20% in 2nd yr and increases by 30% in the 3rd yr. The population after 3 yr is ?
(1) 1716000
(2) 1750000
(3) 1650000
(4) 1600000 

5.    What per cent is 25 paise of Rs 100?
(1) 250%
(2) 25%
(3) 2.5%
(4) 0.25% 

6.    A, B and C undertake to complete a piece of work for Rs 1950. A works for 8 days, B for 9 days and C for 12 days to complete the work. If their daily wages are in the ratio of 3 : 5 : 4, what does C get?
(1) 400
(2) 750
(3) 675
(4) 800 

7.    If 100 men can do 100 jobs in 100 days, then 1 man can do 1 job in
(1) 1 day
(2) 100 days
(3) 50 days
(4) 10 days 

8.    A fruit seller buys mangoes at the rate of 15 for 12 and sells them at the rate of 15 per dozen. Find his gain percentage.
(1) 25.65%
(2) 32.25%
(3) 51.35%
(4) 56.25%

9.    A motorist travels a distance of 10 km at a speed of 50 km/h in the onward journey and 60 km/h while returning. His average speed is
(1) 54 6/11 km/h
(2) 55 km/h
(3) 55 6/11  km/h
(4) 54 km/h

10.  The difference between 90% of a number and 83% of the same number is 175. What is 99% of that number?
(1) 2420
(2) 2475
(3) 2500
(4) 1750

ANSWERS:-
1. (2)
After taking LCM of 4 , 6 , 11 = 132
The students left in each case = 3
Required number of students = 132 + 3 = 135

2. (4)

3. (4)

4. (1)
Initial population = 15,00000;
After first year increment of 10 %, population = 1500000 + 10/100 × 1500000 = 1650000
After second year decrement of 20%, population = 1650000 - 20/100 × 1650000 = 1320000
After increment of 30 % in third year = 1320000 + 30/100 × 1320000 = 1716000

5. (4)

6. (4)
Daily  wages are in the ratio 3 : 4 : 5 , working days of A,B,C = 8,9 and 12 so the wages they get will be in ratio 24 : 45 : 48,
Share of C = 48/(24+45+48) × 1950 = Rs 800

7. (2)

     use chain rule ; if 100 men will do one job in 100 days individually , so one man will do one job in 100 days .

8. (4)
C.P. of one mango = 12/15 = 80 paise ; S.P. of one mango = 15/12=Rs 1.25 ;
Gain = 45 paise , gain = 45/80 × 100 = 56.25 %

9. (1)

    Average speed = (2x×y )/((x+y))=(2 × 50 × 60)/(50 + 60) = 600/11 = 54 6/11 km/hr

10. (2)
value of (90% - 83%)x = 175, 7% of x = 175, 100 % = 2500
99 % of 2500 = 2475

Quant Quiz

Quant Quiz 

1. A constant distance from Chennai to Bangalore is covered by Express  train at 50 km/hr. If it returns to same distance at 40 km/hr. then the average speed during the whole journey is
(a) 45 km/h 
(b) 48 km/h
(c) 45.45 km/h 
(d) 44.44 km/h

2. By selling an article for Rs. 39. a shopkeeper gains 30%. For how much should he sell it to gain 10% ?
(a) 31  
(b) 32.5
(c) Rs 30  
(d) Rs33
3. The two number are in the ratio 2:3 and their product is 54 the sum of the numbers is?
(a) 15  
(b) 5
(c) 9  
(d) 6
4. A Man read 1/3 of a book on day 1. On day 2, he read 1/2 of what he read on first day. 75 pages were left for third day. The number of pages in the book is
(a) 100   
(b) 105
(c) 225  
(d) None of these
5. P can do 2/3 of a job in 8 days and Q is twice as efficient as P. In how many days Q will finish the job
(a) 6  
(b) 8
(c) 12  
(d) 4
6. If A & B together can complete a  piece of work in 15  days & B alone in 20 days, in how many days can A alone complete the work?
(a) 60  
(b) 45
(c) 40  
(d) 30
7. In how many different ways the letter of the word GREATER be arranged?
(a) 5040  
(b) 2520
(c) 1260  
(d) 630
8. In how many years a sum of money will triple itself at 8% per annum simple interest.
(a) 25 years 
(b) 37.5 years
(c) 20 years 
(d) 30 years
9. In how much time a train of length 120 m running at 45km/hr can cross a platform of length 230 m?
(a) 36 sec  
(b) 28 sec
(c) 14 sec  
(d) 18 sec
10. What is 6/11 of 25% of 10% 4400?
(a) 11  
(b) 66
(c) 60  
(d) 36

ANSWERS:-
1. (d)
Average Speed = (2 * 40 * 50)/90 = 44.444 km/hr

2. (d)
Required price = 39 * 1.1/1.3 = 33

3. (a)
Let the numbers be 2x and 3x.
6x² = 54
x = 3
Sum of numbers = 5x = 15

4. (d)
Let the total number of pages be x.
x – x/3 – x/6 = 75
x = 150

5. (a)
P can finish the job in = 3/2 of 8 = 12 days
SO Q will take 12/2 = 6 days to finish the job.

6. (a)
Required number of days = (20 * 15)/(20 - 15) = 60 days

7. (c)
Number of arrangements = 7!/(2! * 2!)

8. (a)
Interest in 1 year = 8%.
To triple the money the interest should be 200%.
Number of years = 200/8 = 25 years.

9. (b)
Crossing time = (120 + 230)/(45 * 5/18) = 28sec

10 . (c)
6/11 of 25% of 10% 4400 = 6/11 * 25/100 * 10/100 * 4400 = 60

Quant : Quiz

Quant : Quiz

1. A fruit seller purchases oranges at the rate of 3 for Rs 5 and selIs them at 2 for Rs 4. His profit in the transaction is:. 
1. 10 %
2. 20 %
3. 15 %
4. 25 %

2.  Raghu bought 4 dozen oranges at Rs 12 per dozen and 2 dozen oranges at Rs 16 per dozen. He soldthem all to earn 20% profit. At what price per dozen did he sell the oranges ?
1. 14.4
2.16.8
3.16
4. 19.2

3. Gopal purchased 35 kg of rice at the rate of Rs 9.50 per kg and 30 kg at the rate of Rs 10 per kg. He mixed the two. Approximately, at what price per kg should he sell the mixture to make 35 % profit in the transaction?.
1.Rs 12
2. Rs 13
3. Rs 12.50
4. None of these

4. An article when sold at a gain of 5% yields Rs 15 more than when sold at a loss of 5%. What is the C.P.. 
1. Rs 64
2.Rs 150
3.Rs 80 .
4.Rs 200

5. A man bought a number of oranges at 3 for a rupee and an equal number at 2 for a rupee. At what price per dozen should he sell them to make a profit of 20 %
1. 4
2. 6
3. 5
4. 7

6. A dealer sold two of his cattle for Rs. 500 each. On one of them he lost 10% on the other, he gained 10%. His gain or loss percent in the entire transaction was:
1. 10% loss
2.1% loss
3. 1% gain
4. Neither loss nor profit

7. A man buys oranges at Rs 5 a dozen and an equal number at Rs 4 a dozen. He sells them at Rs 5.50 a dozen and makes a profit of Rs 50. How many oranges does he buy? .. 
1. 30 dozens
2. 50 dozens
3. 40 dozens
4. 60 dozens

8. When a commodity is sold for Rs 34.80, there is a loss of 25%. What is the cost  price of the commodity?. 
1. 46.40
2, 43
3. 26.10
4. 43.20

9. Ajay bought 15 kg of dal at the rate of Rs 14.50 per kg and 10 kg at the rate of Rs 13 per kg. He mixed the two and sold the mixture at the rate of Rs 15 per kg. What was his total gain in this transaction ?
1. Rs 1.10
2. Rs 11
3. Rs 16.50
4. Rs 27.50

10. If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then the cost of production of a table, the retail price of which is Rs 1265 was :
1. Rs 632.50
2. Rs 814
3. Rs 800
4.Rs 834.34

Answers

1. 2
2. 3
3. 4
4. 2
5. 2
6. 2
7. 2
8. 1
9. 4
10. 3

Speed, Distance and Time tricks

Speed, Distance and Time tricks with Example

Time and Distance
The term times and distance area related to the speed of moving objects 
Speed — We define the speed of an object as the distance covered by it in a unit time interval. 
Speed =(Distance travelled)/(time taken)
⇒  Distance travelled = Speed × time 
⇒ Time =  Distance/Speed 


Unit of measurement 
If distance is measured in kilometer, we measure time in hours and speed is written as km/hr. 

If distance is measured in meter, then time is taken in second and speed written as m/s 

Conversion of unit
1 km/hr = (1000 mtr)/(60×60 seconds)=5/18 m/s
1 m/s =18/5 km/hr

Ex. – A train having length 500 m passes a pole in 30 second. Find the speed of a train (in km/hr) 
⇒Speed=Distance/time=500/30 m/s
=500/30×18/5 km/hr 
= 60 km/hr 

Some useful short cut methods

Last Digit Concepts

Last Digit Concepts with Example

Concept: The last digit of any power

Last digit of any power follow a cycle pattern and repeat after a certain power at a time.

From the above explanation it is clear that after the power of four number of digit will be same.

So find out the last digit we divide the power of any number by 4.

Digit (d)	d^2	d^3	d^4	d^5
1	1	1	1	1
2	4	8	6	2
3	9	7	1	3
4	6	4	6	4
5	5	5	5	5
6	6	6	6	6
7	9	3	1	7
8	4	2	6	8
9	1	9	1	9
0	0	0	0	0

        v The last digit of power of 1 is always 1

v  The last digit of power of 2 repeat in a cycle of 4, 8, 6, 2

v  The digits of powers of 3 repeat in a cycle of 9, 7, 1, 3

v  The last digit of power of 4 repeat in a cycle of 6, 4

v  The last digit of power of 5 & 6 is always same.

v  The last digit of power of 7 repeat in a cycle of 9, 3, 1, 7.

v  The last digit of power of 8 repeat in a cycle of 4, 2,6,8.

v  The digits of powers of 9 repeat in a cycle of 1,9.

Divisiblity Concepts

Divisiblity Concepts with Example Questions

Concept – Divisibility of a number

Divisibility by 2 — A number is divisible by 2 if the unit digit is zero or divisible by 2.

Ex. – 2, 4, 8, 16, 18 etc. are all divisible by 2.

Divisibility by 3 — A number is divisible by 3 if the sum of digits of the number is divisible by 3. 

Ex. – if 43n25 is divisible by 3 then find the minimum value n

Sol. 4+3+n+2+5 is divisible by 3 

So n=1,4,7

Minimum value of n=1 

Divisibility by 4 — A number is divisible by 4 if the number formed by the last two digits is divisible by 4 .

Ex. – 56248 is divisible by 4 since 48 is divisible by 4. 

Divisibility by 5 — A number is divisible by 5 if unit’s digit is 0 or 5. 

Ex. – 1225, 13750, 245 etc. are all divisible by 5. 

Divisibility by 7 — The unit digit of given number is doubled and then it is subtracted from the number obtained after omitting the unit digit. 

If the remainder is divisible by 7 then the given number is also divisible by 7.

 Ex. -is  343 divisible by 7 or not

Sol. Double unit digit 3 of 343 is 6 

Then, 34 – 6 = 28 which is divisible by 7.

Divisibility by 8 — A number is divisible by 8, if the number formed by the last 3 digits is divisible by 8.

Ex. 21056 is divisible by 8, as the number formed by last three digit i.e. 056 is divisible by 8. 

Divisibility by 9 — A number is divisible by 9 if the sum of its digits is divisible by 9.

 Ex. If 256x5 is divisible by 9, find the maximum  value of x 

Sol.   value of x divisible by 9 ⇒(18+x)/9

x=0,9       maximum value of x =9

Divisibility by 10 — An number is divisible by 10 if its last digit is zero 

 Divisibility by 11 — An number is divisible by 11 if the differences of the sum of the digit at odd places and sum of digit at even places is either zero or divisible by 11.

Ex. If 3x4567 is divisible by 11 then what is the value of x

Sol. 3+4+6-x+5+7=0 or divisible by 11

⇒1-x=0  

x=1  

Divisibility by 25 —  A number is divisible by 25 if the number formed by the last two digits is divisible by 25 or the last two digit are zero. 

Divisibility by 125 — A number is divisible by 125 if the number formed by last three digit is divisible by 125 or the last three digit are zero 

Divisibility by Composite number 

Divisibility of Composite number is the divisibility of its Coprime factor 

For Ex. – 

1. divisibility of 33 is divisibility of 3 and divisibility of 11 

2. divisibility of 165 is the divisibility of 3, 5 and 11. 

Time and Work

Quick Study Notes and Quiz on Time and Work

TIPS FOR SOLVING QUESTIONS RELATED TO TIME AND WORK:

1. The total work is taken as 1.

2. If A can do a piece of work in 'n' days, ,then A's 1 day's work is equal to = 1/n

3. If A's 1 day's work = 1/n, then A can complete the work in 'n' days.

4. If A is thrice as good a workman as B, then

    Ratio of work done by A and B = 3 : 1.

    Ratio of time taken by A and B to finish the work = 1 : 3.

5.If ‘M1’ persons can do ‘W1’ work in ‘D1’ days and ‘M2’ persons can do W2 work in D2, days then we have a very general formula in the relationship of M1 D1 W2 = M2 D2 W1. The above relationship can be taken as a very basic and all-in-one formula. We also derive 

A) More men less days and conversely more days less men. 

B) More men more work and conversely more work more men. 

C) More days more work and conversely more work more days. 

6.If we include the working hours (say T1 and T2) for the two groups then the relationship is 

M1 D1 T1 W2 = M2 D2 T2 Q1
Again, if the efficiency (Say E1 and E2) of the persons in two groups is different then the relationship is

M1 D1 T1 E1 W2 = M2 D2 T2 E2 W1

Now, we should go ahead starting with simpler to difficult and more difficult questions. 

Questions on Above Formulaes

1.A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

A. Rs. 375

B. Rs. 400

C. Rs. 600

D.Rs. 800

2. Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?

A. 3 pm

B. 2 pm

C. 1:00 pm

D. 11 am

3. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

A. 20 days

B. 22 1/2days

C. 25 days

D. 30 days

4. P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?

A. 9

B. 11

C. 13

D. 15

5. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:

A. 4 days

B. 5 days

C. 6 days

D. 7 days

6.40 men can cut 60 trees in 8 hours. If 8 men leave the job how many trees wiil be cut in 12 hours?

A. 74

B. 82

C. 72

D. 73

7.A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

A. 8 hours

B. 10 hours

C. 12 hours

D. 24 hours

8. P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?

A. 5 days

B. 10 days

C. 14 days

D. 22 days

9. If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.

A. 12

B. 14

C. 16

D. 18

10. Assume that 20 cows and 40 goats can be kept for 10 days for Rs.460. If the cost of keeping 5 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 50 cows and 30 goats for 12 days?

A. Rs.1104

B. Rs.1000

C. Rs.934

D. Rs.1210

ANSWERS AND SOLUTION :
1(B)Explanation:
C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4 : 3 : 1.
C's share (for 3 days) = Rs. (3 x 1/24 x 3200) = Rs. 400.

2(C)Explanation :
Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the machines were operating.
Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60
Pending work = 1- 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm.

3(B)Explanation:
Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes (3/2 x 60) = 90 days.
So, A takes 30 days to do the work.
A's 1 day's work = 1/30
B's 1 day's work = 1/90
(A + B)'s 1 day's work = (1/30 1/90) = 4/90 = 2/45
So  A and B together can do the work in 45/2 = 22 1/2 days.

4(C)Explanation :
Work done by P in 1 day = 1/23
Let work done by Q in 1 day = q
q × (130/100) = 1/23
=> q = 100/(23×130) = 10/(23×13)
Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13
=> P and Q together can do the work in 13 days

5(A)Explanation:
Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
Then, 6x + 8y = 1/10  and 26x + 48y = 1/2,.
Solving these two equations, we get : x = 1/100 and y = 1/200 .
(15 men + 20 boy)'s 1 day's work = (15/100 + 20/200) = 1/4
So,  15 men and 20 boys can do the work in 4 days.

6(C) Explanation
By basic formula:
M1 = 40, D1 = 8, W1 = 60(cutting of trees is taken as work)
M2 = 40 - 8 = 32, D = 12, W2 = ?
Putting the values in the formula
M1 D1 W2 = M2 D2 W1
We have , 40 x 8 x W2 = 32 x 12 x  60
or, W2 = (32 x 12 x 60)/(40 x 8) = 72

7(C)Explanation:
A's 1 hour's work = 1 /4 ;
(B + C)'s 1 hour's work = 1/3 ;
(A + C)'s 1 hour's work = 1/2 .
(A + B + C)'s 1 hour's work = (1/4  + 1/3) = 7/12
B's 1 hour's work = (7/12 - 1/2) = 1/12 .
So, B alone will take 12 hours to do the work.

8(B)Explanation :
Work done by P in 1 day = 1/20
Work done by Q in 1 day = 1/12
Work done by P in 4 days = 4 × (1/20) = 1/5
Remaining work = 1 – 1/5 = 4/5
Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15
Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6
Total days = 4 + 6 = 10

9(C)Explanation :
Wages of 1 woman for 1 day = (21600)/(40 x 30)
Wages of 1 man for 1 day = (21600×2)/(40×30)
Wages of 1 man for 25 days = (21600×2×25)/(40×30) = 1080000/1200=900
Number of men = 14400/900 =16

10(A)Explanation :
Assume that cost of keeping a cow for 1 day = c ,
cost of keeping a goat for 1 day = g
Cost of keeping 20 cows and 40 goats for 10 days = 460
Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46
=> 20c + 40g = 46
=> 10c + 20g = 23 ---(1)
Given that 5g = c
Hence equation (1) can be written as 10c + 4c = 23 => 14c =23
=> c=23/14
cost of keeping 50 cows and 30 goats for 1 day
= 50c + 30g
= 50c + 6c (substituted 5g = c)
= 56 c = 56×23/14
= 92
Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104

Time and Distance

Short Notes on Time and Distance

TIPS AND FORMULAS ON TIME AND DISTANCE:

1. Speed =  Distance/Time

2. Time =  Distance /Speed

3. Distance = Speed x Time

4. km/hr to m/s conversion:
1 kmph =   5/18 m/s
5. m/s to km/hr conversion:

 1 m/s =   18/5 m/s

6. If the ratio of speeds of train A and B is a : b, then the ratio of time taken by them to cover the same distance = b : a.

7. If a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,the average speed during the whole journey is
2xy/(x + y) km/h

8. The time taken by a train in passing a pole or standing man is the same as the time taken by the train to cover a distance equal to its own length.

9. The time taken by a train of length 'L' metres in passing a stationary object of length 'B' metres is equal to the time taken by the train to cover a distance equal to (L + B) m.

10. If two trains are moving in the same directions at u m/s and v m/s, where u > v, then their relative speed will be equal to the difference of their speeds i.e. (u - v) m/s.

11. If two trains are moving in the opposite directions at u m/s and v m/s, then their relative speed will be equal to the sum of their speeds i.e. (u + v) m/s.

12.If two trains of length 'a' metres and 'b' metres are moving in the same directions at u m/s and v m/s respectively, then: 

The time taken by the faster train to cross the slower train is

 (a + b)/(u - v) sec.

13.If two trains of length 'a' metres and 'b' metres are moving in the opposite directions at u m/s and v m/s respectively, then:

The time taken by the faster train to cross the slower train is

 (a + b)/(u + v) sec.

14.If two trains start at the same time from points A and B towards each other and after crossing they take 'a' and 'b' hour in reaching B and A respectively, then:

(A's speed) : (B's speed) = Öb : Öa

Questions based on above formula:
1.A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is

A. 11 hrs

B. 8 hrs 45 min

C. 7 hrs 45 min

D. 9 hrs 20 min

2. Two men P and Q start a journey from same place at a speed of  3 1/2 km/hr and 3 km/hr  respectively. If they move in the same direction then what is the distance between them after 4 hours?

A.  3 km

B.  2 1/2 km

C.  2 km

D. 3 1/2 km

3.A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

A. 100 kmph

B. 110 kmph

C. 120 kmph

D. 130 kmph

4. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

A. 12

B. 11

C. 10

D. 9

5. A student walks from his house at 4 km/hr and reaches his school 5 minutes too late. If his speed had been 5 km/hr, he would have reached 10 minutes too early. The distance of the school from his house is:

A.  5/3 km

B. 5/27 km

C. 5 km

D.  5/9 km

6. In a journey of 160 km, a train covers the first 120 km at a speed of 80 km/h and the remaining distance at 40 km/h. The average speed of the train for the whole journey is:

A.  60 km/h

B.  64 km/h

C.  68 km/h

D.  72 km/h

7. Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?

A. 17 hr

B. 14 hr

C. 12 hr

D. 19 hr

8. A tractor is moving with a speed of 20 km/h, x km ahead of a truck moving with a speed of 35 km/h. If it takes 20 minutes for the truck to overtake the tractor, then x is equal to:

A.  5 km

B.  10 km

C.  15 km

D.  20 km

9. By walking at 4/5  of his normal speed, a man reaches his office 10 minutes late. How much time he normally takes to reach his office?

A.  40 minutes

B.  45 minutes

C.  50 minutes

D.  60 minutes

10. Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?

A. 1 hr 42 min

B. 1 hr

C. 2 hr

D. 1 hr 12 min

ANSWERS AND SOLUTION:
1(C)Explanation :
Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min

2(C)Explanation:
If two trains are moving in the same directions at u m/s and v m/s, where u>v, then their relative speed will be equal to the difference of their speeds i.e.(u - v) m/s
Let u = 3 1/2 km/hr and v = 3 km/hr
Thus, Relative  speed = 3 1/2 - 3
= 1/2 km/hr
Therefore, Required distance = Speed x Time = 1/2 x 4
= 2 km

3(C)Explanation:
Let speed of the car be x kmph.
Then, speed of the train = 150/100 x = 3/2 x kmph.
So 75/x - 75/(3/2)x = 125/(10 x 60)
=> 75/x - 50/x = 5/24
=> x = (25 x 24)/5 = 120 kmph.

4(C)Explanation :
speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distance/speed = 9/54 hour =1/6 hour = 60/6 min=10 min

5(C)Explanation:
Let the distance of the school from his house be x km.
Time = Distance/Speed
So x/4 - x/5 = 15/60
or, (5x - 4x)/20 - 1/4
or, x = 5 km

6(B)Explanation:
Time = Distance/Speed
Total time taken for the journey = 120/80 + 40/40 = 5/2 hours
So, Average speed = 160 x 2/5
= 64 km/hr

7(A)Explanation :
Relative speed = 5.5 - 5 = .5 kmph (because they walk in the same direction)
distance = 8.5 km
time = distance/speed=8.5/.5=17 hr

8(A)Explanation:
Distance = Speed x Time
Distance covered by the truck in 20 minutes = 35 x 20/60 =  35/3 km
Distance covered by the tractor in 20 minutes = 20 x 20/60 =  20/3 km
So 20/3 + x = 35/5
or, x = 5 km

9(A)Explanation:
Walking at 4/5 of the normal speed means that the time taken would be 5/4 of the normal time.
Let the normal time taken to reach the office be "t" minutes,
So 5/4t - t 10 minutes
or , t/4 = 10
or, t = 40 minutes

10(D)Explanation :
New speed = 6/7 of usual speed
Speed and time are inversely proportional.
Hence new time = 7/6 of usual time
Hence, 7/6 of usual time - usual time = 12 minutes
=> 1/6 of usual time = 12 minutes
=> usual time = 12 x 6 = 72 minutes = 1 hour 12 minutes