KRISHNA MOHAN

Monday, 14 August 2017

Quant Quiz on Percentage

1. Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are

(a) 36, 46

(b) 42, 33

(d) None of these

2. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

(a) 600 Apples

(b) 700 Apples

(d) None of these

3. What percentage of numbers from 1 to 70 has 1 or 9 in the unit's digit?

(a) 20

(b) 22

(d) None of these

4. If A = x% of y and B = y% of x, then which of the following is true?

(a) A is smaller than B.

(b) A is greater than B

(d) None of these

5. In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?

(a)50

(b)100

(d)72

6. A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

(a)34%

(b)44%

(d)64%

7. In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

(a) 3000

(b)2700

(d) 3500

8. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

(a) 57%

(b)60%

(d) 90%

9. Helen went to the stationers and bought things worth Euro 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) Euro 15

(b) Euro 15.7

(d) Euro 20

10. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

(a) 4.37%

(b) 5%

(d) 8.75%

Answer With Explanation

1. (b)

Explanation: Let their marks be (x + 9) and x.

Then, x + 9 = 56/100(x + 9 + x)

25(x + 9) = 14(2x + 9)

3x = 99

x = 33

So, their marks are 42 and 33.

2. (b)

Explanation: Suppose originally he had x apples.

Then, (100 - 40)% of x = 420.

60/100 x x = 420

x = (420 x 100)/60 = 700

3. (a)

Explanation: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1.

Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

Number of such number =14

Required percentage = (14/70 x 100)% = 20%.

4. (d)

Explanation: x% of y = (x/100 x y) = (y/100 x x) = y% of x

A = B.

5. (b)

Explanation: Let the number of students be x.

Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x.

80% of x = 48 + 2/3 of 48

80/100x = 80

x = 100.

6. (d)

7. (b)

Explanation: Number of valid votes = 80% of 7500 = 6000.

Valid votes polled by other candidate = 45% of 6000

= (45/100 x 6000) = 2700.

8. (a)

Explanation: Total number of votes polled = (1136 + 7636 + 11628) = 20400.

Required percentage = (11628/20400 x 100)% = 57%.

9. (c)

Explanation: Let the amount taxable purchases be Euro x.

Then, 6% of x = 30/100

x = (30/100 x 100/6) = 5.

Cost of tax free items = Euro [25 - (5 + 0.30)] = Euro 19.70

10. (b)

Explanation: Increase in 10 years = (262500 - 175000) = 87500.

Increase% = (87500/175000 x 100)% = 50%.

Required average = (50/10)% = 5%.

QUANT QUIZ

(1) The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

1. 58

2. 48

3. 30

4. 20

(2) The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

1. 17 : 18

2. 8 : 9

3. Cannot be determined

4. 21 : 22

(3) A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is

1. 4:5

2. 9:5

3. 8:5

4. 9:2

(4) How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?

1. 36 kg

2. 42 kg

3. 54 kg

4. 63 kg

(5) 8 litres are drawn from a cask full of wine and is then filled with water.This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

1. 18 litres

2. 24 litres

3. 32 litres

4. 42 litres

(6) The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?

1. Rs. 2000

2. Rs. 2200

3. Rs. 2400

4. Data inadequate

(7) The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?

1. Rs. 2000

2. Rs. 2200

3. Rs. 2400

4. Data inadequate

(8) In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?

1. 67 kg.

2. 68 kg.

3. 69 kg.

4. Data inadequate

(9) A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?

1. 26 minutes and 18 seconds

2. 42 minutes and 36 seconds

3. 45 minutes

4. 46 minutes and 12 seconds

(10) There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?

1. Rs. 2160

2. Rs. 3120

3. Rs. 3972

4. Rs. 6240

ANSWERS WITH SOLUTIONS:

(1) 3

(2) 4

(3) 2 dog : hare = 3*3 leaps of hare :5*1

9:5

(4) 4

(5) Let the quantity of the wine in the cask originally be x litres.

Then, quantity of wine left in cask after 4 operations = [x(1-8/X)⁴]litres

= [x(1-8/X)⁴] = 16/81

x = 24

(6) 1

(7) 1

(8) 1 Let Arun's weight by X kg.

According to Arun, 65 < X < 72

According to Arun's brother, 60 < X < 70.

According to Arun's mother, X <= 68

The values satisfying all the above conditions are 66, 67 and 68.

Required average = 66 + 67 + 68/3 = 201/3 = 67 kg.

(9) 4

L.C.M. of 252, 308 and 198 = 2772.

So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.

(10) 3

Quantitative Aptitude Quiz

(Directions: 1-5): Study the following bar charts carefully and answer the questions asked below.

Foreign Trade (Imports and Exports) by various countries

1. The ratio of the maximum exports to the minimum imports was closest to ?
(a) 64
(b) 69
(c) 74
(d) 79

2. How many countries exhibited a trade surplus ?
(a) 5
(b) 3
(c) 4
(d) 6

3. The total trade deficit/surplus for all the countries (together) was ?
(a) 11286 surplus
(b) 11286 deficit
(c) 10286 deficit
(d) 10286 surplus

4. The highest trade deficit was shown by which country ?
(a) C
(b) G
(c) H
(d) L

5. The ratio of exports to imports was highest for which country ?
(a) I
(b) A
(c) J
(d) K

6. If the sum of two numbers is 55 and the HCF and LCM of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
(a) 55/601
(b) 601/55
(c) 11/120
(d) 120/11

7. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

(a) 28 4/7 years

(b) 31 5/7 years

(d) None of these

8. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 cubic metre, then the rise in the water level in the tank will be:

(a) 20 cm

(b) 25 cm

(d) 50 cm

9. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs.6500 for 6 months, B, Rs.8400 for 5 months and C, Rs.10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs.7400. Calculate the share of B in the profit.

(a) Rs.1900

(b) Rs.2660

(d) Rs.2840

10. 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

(a) 18 litres

(b) 24 litres

(d) 42 litres

ANSWERS:

1. (b)
The value of maximum exports = 6045.
The value of minimum imports = 87.
Therefore, the required ratio (6045/8)= 69.48 = 69 (approximately).

2. (c)
Out of a total of 12 countries, 8 showed a deficit while 4 showed a surplus.

3. (b)
Exports= 25625
Imports= 36911
Sum of exports - Sum of imports = deficit (11286).

4. (d)
Visually its clear that L has the highest trade deficit.

5. (a)
I has a ratio of 4002/2744 = 1.45, which is the highest.

6. (c)
Let the numbers be a and b.
Then, a+b= 55 and ab= 5*120= 600.
So the required sum= (1/a)+ (1/b)= (a+b)/ab=55/600= 11/120

7. (b)
Required average= (67*2+35*2+6*3)/(2+2+3)
= (134+70+18)/(7)
= 222/7
= 31 5/7 years

8. (b)
Total volume of water displaced= (4*50) cubic metre= 200 cubic metre
Rise in water level = (200/40*20)m= 0.25m= 25cm.

9. (b)
For managing, A received = 5% of Rs.7400= Rs.370
Balance= Rs.(7400-370)= Rs.7030
Ratio of their investments= (6500*6):(8400*5):(10000*3)= 39000:42000:30000
= 13:14:10
So, B's share= Rs.[7030*(14/37)] = Rs.2660

10. (b)
Let the quantity of the wine in the cask originally be x litres.
Then, quantity of wine left in cask after 4 operations= [x{1-(8/x)^4}] litres
So, [x{1-(8/x)}^4]/x= 16/81
= [1-(8/x)]^4=(2/3)^4
= (x-8)/x=2/3
= 3x-24= 2x

= x=24

Time and Work

1. 12 Men work 9h/ day to complete 40% of the work in 30 day. The rest work is done by 15 men,6h / day. Then workdone in how many days.
(a) 45
(b) 54
(c) 47
(d) None of these

2. 120 workers can complete a piece of work in 85 days and each worker works 10h/day. All worker start the work, after 10 day all goes to strike. Due to strike, 25 day work stop. How many more worker employed to finish the remaining work if each worker works 8h / day.
(a) 105
(b) 75
(c) 101
(d) 100

3. In a hotel , food material available for 200 student for 50 days. After 10 days , 50 more students join the hostel. The rest food material a available for how many days.
(a) 22 days
(b) 25
(c) 32 days
(d) None of these

4. 12 male complete a piece of work in 4 days. 15 female complete the same work in 4 days. 6 male start the work. After 2 days all male left the work. How many female required to finish the remaining work complete in 3 days.
(a) 20
(b) 15
(c) 10
(d) None of these

5. Work of 4 male is equal to work of 6 female and 9 female is equal to 12 Boys. 8 male and 6 female together work 8 hr/day to complete a work in 15 days. 2 male and 3 female and 4 Boy together work 6hr/day to complete that work so how many day will taken by them.
(a) 30 days
(b) 40 days
(c) 34 days
(d) None of these

6. A , B can do a work in 20 and 30 days. Starting with A work doing by alternate day then in how many days work completed.
(a) 20
(b) 10
(c) 24
(d) 14

7. A , B, C along complete a work in 15 , 20 and 30 days. All together start the work, After 4 days, A left the work, Next after 4 days B left the work. Rest work done by c. they got Rs. 4500 for whole work. Find the share of B
(a) Rs. 1000
(b) Rs.1800
(c) Rs. 2000
(d) RS.3000

8. A, B, C fill a tank in 15, 20 & 30 hr. All pipe opened together. After sum hours closed the pipe A. After 1 hour close the pipe B. The rest work done by C in 5 hour. Then how many times pipe A was closed
(a) 10
(b) 5
(c) 3
(d) 4

9. Two inlet pipe A & B can fill the tank in 20 & 30 hr. Starting by A both pipe open alternately. So tank will be fill after how many time?
(a) 24 hr
(b) 20 hr
(c) 30 hr
(d) None of these

10. Two inlet pipe A & B can fill a tank in 25 min & 20 min. But due to same disturbance in pipe, 5/6th from pipe A, & 2/3rd form pipe B water flow. Both pipe fill the tank in how many min?
(a) 15 min
(b) 20 min
(c) 10 min
(d) None of these

ANSWERS WITH SOLUTIONS

1. (b) Men 1*day1*hour1/work1 = Men2*day2*hour2/work2
12*30*9/40% = 15*days*6//60%
days = 54

2. (a) Men1*day1*hour1/work1 = Men2*day2*hour2/work2
120*85*10 = (120*10*10 + 50*x*8)
x = 225 men
so more worker required 225-120 = 105

3. (c) Initial student*remaining days = after joining total student* x
200*40 = 250* x
x = 32 days
4. (b)12m ------> 4 15 F -----> 4
So 12m * 4 = 15F * 4
4 m = 5F
1m = 5/4 f
Let take F = x
So 6m * 2 + xF * 3 = 15F * 4
x = 15
5. (b)4m = 6F
2m = 3F
Similarly
9F = 12B
3F = 4B
Work completed by
( 8 M x 6F) x 8 x 15 = ( 2M + 3F + 4B) x 6 xD
D= 40 days
6.(c)

7.(b) A ‘s 4 days work = 4 x 4 = 16
B’s 8 days work = 3 x 8 = 24
Remaining work = 60 – 24 – 16 = 20
20’ wo rk complete by C in = 10
So A: B: C = 16: 24: 20
So share of B = Rs. 1800
8.(b)A = 15
B = 20
C = 30
Unit by A, B and C is 4, 3, 2
C’s work = 2 x 5 = 10
B’s = 5
Remaining work = 60 – 15 = 45
This work done by A + B + C = 45/9 = 5 hrs.
A was closed after 5 hrs.

9.(a) Pipe A contribution = 1/20
pipe B contribution = 1/30
A + B = 1//20 + 1/30 = 5/60
1/12= 12 days *2= 24 days

10. (a) water flows from pipe A = 25*6/5
water fows from pipe B = 20*3/2
A + B = 1/30 +1/30 = 2/30
so taank filled by A+B = 15 mins.

KRISHNA MOHAN

Pages

Monday, 14 August 2017

Quant Quiz on Percentage

Quant Quiz on Percentage

QUANT QUIZ

QUANT QUIZ

Quantitative Aptitude Quiz

Quantitative Aptitude Quiz

Time and Work

Time and Work

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