Quantitative Aptitude

Q1. A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two-thirds the time needed by the second pair to complete the work. Which is the first pair?

(a) A and B

(b) A and C

(c) B and C

(d) A and D

(e) C and D

Ans.(d)

Sol. Work done in one day by A, B and C are 1/4,1/8,1/16 and 1/32 respectively.

Using answer choices, we note that the pair of B and C does 3/16 of work in one day; the pair of A and D does 1/4+1/32=9/32 of work in one day

Hence, A and D take 32/9 days

B and C take 16/3=32/6 days

Hence, the first pair must comprise of A and D

Directions (2-6): Read the passage below solve the questions based on it.

There are infinite pipes attached to a very big tank. Pipes are numbered like P₁,P₂,P₃………… and so on. Its also known that efficiency of every subsequent pipe is half the efficiency of earlier pipe, i.e., efficiency of P₂ pipe is half the efficiency of P₁ pipe and so on. However, in case of P₁ pipe, this rule is not true since there is no earlier pipe. When all the pipes are working together, the tank gets filled in 2 hours.

Q2. How much time will P₄ take of fill the tank working alone?

(a) 8 h

(b) 16 h

(c) 32 h

(d) 4 h

(e) Cannot be determined

Ans.(c)

Sol. Pipe P_4 will take 32 hours. Hence, option (c) is the answer.

When all the pipes are used together, tank gets filled in 2 hours. Hence in one hour, tank get ½ = 50% filled.

Assume that pipe P_1 fills x% of the tank in one hour.

So, pipe P_2 fills x/2% of the tank in one hour; pipe P_3 fills x/4% of the tank in one hour and so on.

According to the question,

x+x/2+x/4+ ………………………….. till infinity = 50%

This is an infinite GP.

Sum of infinite GP = a/(1 - r)=x/(1 - 1/2) = 2x

Hence 2x = 50% ⇒ x = 25%

So, 1st tank fills 25% of the tank in One hour. Hence 1st tank fills the tank in 100/25 = 4 hrs.

So, 2nd pipe fills the tank in 8 hours; 3rd pipe fills the tank in 16 hours and so on.

Q3. What is difference in the time taken by P₅ and P₆?

(a) 32 h

(b) 64 h

(c) 128 h

(d) 16 h

(e) Cannot be determined

Ans.(b)

Sol. Pipe P₅ will take 64 hours and Pipe P₆ will take 128 hours.

Hence difference in the time taken = 64 hours. Hence, option (b) is the answer.

When all the pipes are used together, tank gets filled in 2 hours. Hence in one hour, tank get ½ = 50% filled.
Assume that pipe P_1 fills x% of the tank in one hour.
So, pipe P₂ fills x/2% of the tank in one hour; pipe P₃ fills x/4% of the tank in one hour and so on.
According to the question,
x+x/2+x/4+ ………………………….. till infinity = 50%
This is an infinite GP.
Sum of infinite GP = a/(1 - r)=x/(1 - 1/2) = 2x
Hence 2x = 50% ⇒ x = 25%
So, 1st tank fills 25% of the tank in One hour. Hence 1st tank fills the tank in 100/25 = 4 hrs.

So, 2nd pipe fills the tank in 8 hours; 3rd pipe fills the tank in 16 hours and so on.

Q4. How many pipes can fill the tank within 100 hours working alone?

(a) 4

(b) 5

(c) 6

(d) 7

(e) Infinite

Ans.(b)

Sol. From pipe P1 to pipe P5, each of the pipes can fill the tank independently within 100 hours. Hence 5 pipes can till the tank independently within 100 hours. Hence, option (b) is the answer.

When all the pipes are used together, tank gets filled in 2 hours. Hence in one hour, tank get ½ = 50% filled.

Assume that pipe P_1 fills x% of the tank in one hour.

So, pipe P2 fills x/2% of the tank in one hour; pipe P3 fills x/4% of the tank in one hour and so on.

According to the question,

x+x/2+x/4+ ………………………….. till infinity = 50%

This is an infinite GP.

Sum of infinite GP = a/(1 - r)=x/(1 - 1/2) = 2x

Hence 2x = 50% ⇒ x = 25%

So, 1st tank fills 25% of the tank in One hour. Hence 1st tank fills the tank in 100/25 = 4 hrs.

So, 2nd pipe fills the tank in 8 hours; 3rd pipe fills the tank in 16 hours and so on.

Q5. Due to some technical problem, only four pipes P₁,P₂,P₃ and P₄ are in working condition. These pipes are now paired up to obtain two pairs of pipes. Now it is found that one pair of pipe is taking 2/3rd of the time taken by the other pair to fill the tank independently. Which of the following is one of the two pairs?

(a) P₁,P₂

(b) P₁,P₃

(c) P₁,P₄

(d) P₂,P₄

(e) Cannot be determined

Ans.(c)

Sol. Efficiency of pipe P1 = 25%, Efficiency of pipe P2= 12.5%, Efficiency of pipe P3 = 6.25%, Efficiency of pipe P4 = 3.12%. If we club (pipe P1 and pipe P4) in one group and (pipe P2 and pipe P3) in other group, it satisfies the condition. Hence, option (c) is the answer.

When all the pipes are used together, tank gets filled in 2 hours. Hence in one hour, tank get ½ = 50% filled.
Assume that pipe P1 fills x% of the tank in one hour.
So, pipe P2 fills x/2% of the tank in one hour; pipe P3 fills x/4% of the tank in one hour and so on.
According to the question,
x+x/2+x/4+ ………………………….. till infinity = 50%
This is an infinite GP.
Sum of infinite GP = a/(1 - r)=x/(1 - 1/2) = 2x
Hence 2x = 50% ⇒ x = 25%
So, 1st tank fills 25% of the tank in One hour. Hence 1st tank fills the tank in 100/25 = 4 hrs.

So, 2nd pipe fills the tank in 8 hours; 3rd pipe fills the tank in 16 hours and so on.

Q6. How much time will P₂ take to fill the tank working alone?

(a) 4

(b) 8

(c) 16

(d) 32

(e) 12

Ans.(b)

Sol. Pipe P2 will take 8 hours in filling the tank. Hence, option (b) is the answer.

When all the pipes are used together, tank gets filled in 2 hours. Hence in one hour, tank get ½ = 50% filled.
Assume that pipe P1 fills x% of the tank in one hour.
So, pipe P2 fills x/2% of the tank in one hour; pipe P3 fills x/4% of the tank in one hour and so on.
According to the question,
x+x/2+x/4+ ………………………….. till infinity = 50%
This is an infinite GP.
Sum of infinite GP = a/(1 - r)=x/(1 - 1/2) = 2x
Hence 2x = 50% ⇒ x = 25%
So, 1st tank fills 25% of the tank in One hour. Hence 1st tank fills the tank in 100/25 = 4 hrs.

So, 2nd pipe fills the tank in 8 hours; 3rd pipe fills the tank in 16 hours and so on.

Q7. Ram finishes a work in 7 days. Rahim finishes the same job in 8 days and Robert in 6 days. They take turns to finish the work. Ram worked on the first day, Rahim on the second day and Robert on the third and then again Ram and so on. Who was working on the last day when work got finished?

(a) Ram

(b) Rahim

(c) Robert

(d) Rahim and Robert

(e) Cannot be determined

Ans.(a)

Sol. Three day’s work = 1/7+1/8+1/6=73/168

Six day’s work = 73/84

Seventh day work = 1/7, done by Ram

Since 73/84+1/7=85/84 > 1, therefore, Ram was working on the last day.

Q8. Construction of a road was entrusted to a civil engineer. He has to finish the work in 124 days for which he employed 120 workers. Two-third of the work was completed in 64 days. How many workers can be reduced now without affecting the completion of the work on time?

(a) 56

(b) 64

(c) 80

(d) 24

(e) None of these

Ans.(a)

Sol. 2/3rd of the work was completed in 64 days by 120 workers.

1/3rd of the work was completed in 32 days by 120 workers.

Also 1/3rd of the work is to be completed in 60 days by (120 – x) workers, where x is the number of men reduced in order to finish the work on schedule.

So, (120 – x) × 60 = 120 ⇒ x = 56

Q9. Two workers earned Rs. 225 first worked for 10 days and the second for 9 days. How much did each of them get daily if the first worker got Rs. 15 more for working 5 days than the second worker got for working 3 days?

(a) Rs. 11.70; Rs. 12.00

(b) Rs. 10.80; Rs. 13.00

(c) Rs. 11.25; Rs. 12.50

(d) Rs. 12.60; Rs. 11.00

(e) None of these

Ans.(b) Sol. Let A got Rs. x per day and B got Rs. y per day. So, 10x + 9y = 225 and 5x = 3y + 15 ⇒ x = 10.80, y = 13.

Q10. Two pipes A and B can fill a tank in 20 and 30 h respectively. Both the pipes are opened to fill the tank but when the tank is 1/3 full, a leak develops in the tank. Due to this leakage one-third of the water supplied by pipes A and B goes waste. What is the total time to fill the tank if the leak if not closed?

(a) 12 h

(b) 16 h

(c) 18 h

(d) 20 h

(e) None of these

Ans.(b)

Sol. Let us assume total work = 180 (we are not assuming it to be LCM of 20 and 30 = 60 because in that case 1/3rd of A + B will be fractional)

Time taken to fill 1/3rd of the tank = 180/ (9 + 6) = 4 h

Due to leakage, net inflow = 2/3 (9 + 6) = 10 units

Time taken to fill remaining 120 units = 12 h

So total time taken = 12 + 4 = 16 h

Q11. In how many days will 10 men finish the job? To answer the question which of the following information(s) is/are sufficient (assume equal efficiency of work)?

A. 20 men can finish the same job in 20 days.

B. 40 men can finish the job in 1/4 time of what 10 men take.

C. 50 men can finish double the job in 16 days.

(a) Only (A) alone is sufficient

(b) Only (C) alone is sufficient

(c) Any one of (A), (B), (C) alone is sufficient

(d) (A) and (B) together or (C) alone is sufficient

(e) (A) or (C) alone is sufficient

Ans.(e)

Sol. (A) alone: (Use M1 D1=M2 D2)

10 × N = 20 × 20 ⇒ N = 40 days.

(C) alone: (Use M1 D1 W2=M2 D2 W1)

10 × N × 2 = 50 × 16 × 1 ⇒ N = (50 × 16)/20 = 40 days

Statement B provides the same information as given in the question.

Q12. In how many days will 22 men finish the work?

A. 6 women and 8 men can finish a work in 10 days.

B. 6 women work as much as 3 men in the same time.

C. Each women takes twice more time taken by a man to finish the work.

(a) A alone is sufficient

(b) A and B together are only sufficient

(c) A and either B or C together are sufficient

(d) All A, B and C together are necessary

(e) All even together are not sufficient

Ans.(c)

Sol. 2 women = 1 man

(6 women + 8 men) = 3 + 8) men = 11 men

⇒ (11 × 10)/12 = 12 days

Q13. Amit can do a job in 9 days. To find the number of days in which Gagan can do the same job, which of the following information(s) is/are necessary / sufficient?

P. Gagan is 50% more efficient than Amit.

Q. Amit and Gagan together can do the job in 3(3/5) days.

R. Amit is 33(1/3)% less efficient than Gagan.

(a) Only P alone is sufficient

(b) Only q alone is sufficient

(c) Only either P or Q is sufficient

(d) Any one of the three statements is sufficient

(e) All the three statements are necessary

Ans.(d)

Sol. Since Ganga is 50% more efficient than Amit, he will do the job in 9

(100/(100+50))=9 2/3 = 6 days

From statement Q:

Ganga will do the job in (18/5×9)/(9-18/5)=(18×9)/(45-18)

=(18×9)/27=6 days

From statement R:

Ganga will do the job in ((100-100/3)/10)=9(200/300) 

= 6 days

Directions (14-15): Read the passage below and solve the questions based on it.

Tank at a water supply station is filled with water by several pumps. At first, three pumps of the same capacity are turned on; 2.5 h later, two more pumps (both the same) of a different capacity are set into operation. After 1 h, the additional pumps were set into operation; the tank was almost filled to its capacity (15 m^3 were still lacking); in another hour the tank was full. One of the two additional pumps could have filled the tank in 40 h.

Q14. What is the volume of the tank?

(a) 60 m^3

(b) 80 m^3

(c) 75 m^3

(d) 90 m^3

(e) None of these

Ans.(a)

Sol. Given that, in the last hour, tank lacks 15 m^3. Hence 25% of the tank = 15m^3. Hence 100% of the tank = 60m^3.

Hence, option (a) is the answer.

Assume that the three pumps initially put are named pump A and two pumps added later on are named pump B.

Assume the percentage of tank filled in by one pump A = y% per hour.

Hence total percentage of tank filled in three pumps in one hour = 3y% per hour.

Hence total percentage of tank filled in three pumps in 2.5 hours = 2.5 × 3y% = 7.5y%

After 2.5 hours, 2 more pumps (both same) of a different capacity are set into operation. Given that “one of the two additional pumps could have filled the tank in 40 hours”. Hence percentage of tank fill in by one pump B = (100%)/40 = 2.5% per hour.

Hence total percentage of tank filled by two pumps B in one hour = 2 × 2.5 % per hour = 5% per hour.

Hence total percentage of tank filled by two pumps B in two hours = 2 × 5% per hour = 10 % per hour.

So, 90% of the tank is filled in by pipes A in (2.5 + 1 + 1) hrs. = 4.5 hrs.

So, in One hour, percentage of tank filled by 3pipes A = (90%)/4.5 = 20% per hour

Hence in one hour, total percentage of tank filled by (3 pipes A and 2 pipes B) together = 20% + 5% = 25%

Q15. How much water does one of the first three pumps emit in an hour?

(a) 5 m^3

(b) 4 m^3

(c) 3 m^3

(d) 2 m^3

(e) None of these

Ans.(b)

Sol. In One hour, percentage of tank filled by 3 pipes 

A = (90%)/4.5 = 20% per hour

Hence, in One hour, percentage of tank filled by 1 pipe 

A = (20%)/3 per hour

Since 100% of the tank = 60m^3 ⇒ 1% of the tank = 0.6 m^3 

⇒ (20%)/3 of the tank = 20/3 × 0.6 = 4 m^3. 

Hence, option (b) is the answer.

Assume that the three pumps initially put are named pump A and two pumps added later on are named pump B.

Assume the percentage of tank filled in by one pump A = y% per hour.

Hence total percentage of tank filled in three pumps in one hour = 3y% per hour.

Hence total percentage of tank filled in three pumps in 2.5 hours = 2.5 × 3y% = 7.5y%

After 2.5 hours, 2 more pumps (both same) of a different capacity are set into operation. Given that “one of the two additional pumps could have filled the tank in 40 hours”. Hence percentage of tank fill in by one pump B = (100%)/40 = 2.5% per hour.

Hence total percentage of tank filled by two pumps B in one hour = 2 × 2.5 % per hour = 5% per hour.

Hence total percentage of tank filled by two pumps B in two hours = 2 × 5% per hour = 10 % per hour.

So, 90% of the tank is filled in by pipes A in (2.5 + 1 + 1) hrs. = 4.5 hrs.

 

So, in One hour, percentage of tank filled by 3pipes A = (90%)/4.5 = 20% per hour

Hence in one hour, total percentage of tank filled by (3 pipes A and 2 pipes B) together = 20% + 5% = 25%

Quantitative Aptitude

Q1. For two consecutive years, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the second year is Rs. 42000 and my expenses in the first year in Rs. 21000, my total savings for the two-year is
(a) Rs. 5,000
(b) Rs. 10,000
(c) Rs. 12,000
(d) Rs. 15,000
(e) None of these

Q2. Two-third of the boys and three-fourth of the girls of a school participate in a function. If the number of participating students is 550, out of which 150 are girls, what is the total number of students in the school?
(a) 500
(b) 550
(c) 600
(d) 750
(e) 800

Q3. Rupesh was thrice as old as Ravi 6 years back. He will be 5/3 times as old as Ravi 6 years hence. How old is Ravi today?
(a) 24 years
(b) 18 years
(c) 12 years
(d) Cannot be determined
(e) None of these

Q4. 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24 days. If 8 more cows and 9 more buffaloes are brought in, how long will the fodder last?
(a) 20 days
(b) 18 days
(c) 16 days
(d) 21 days
(e) None of these

Q5. Ajay opened a shop investing Rs. 30000. Anju joined him 2 months later, investing Rs. 45000. They earned a profit of Rs. 54000 after completion of one year. What will be Anju’s share of profit?
(a) 28000
(b) 20000
(c) 31000
(d) 30500
(e) None of these

Q6. On sports day, if 30 children were made to stand in a column, 16 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed?
(a) 20
(b) 21
(c) 22
(d) 18
(e) None of these

Q7. On a test consisting of 30 questions. Number of wrong answers is 50 percent less than number of right answers. Each answer was either right or wrong. What is the ratio of right answers to wrong answers?
(a) 3:2
(b) 4:1
(c) 5:1
(d) 2:1
(e) None of these

Q8. A and B invested the same capital in a business. At the year-end they share the profit in the ratio 3:2. If A has invested his capital for whole year, for how many months B has invested his capital?
(a) 6 months
(b) 8 months
(c) 9 months
(d) 5months
(e) None of these

Q9. Anshu and Brawn have incomes in the ratio 5:3. The expenses of Anshu, Brawn and Chen are in the ratio 8:5:3. To find the income of Anshu, which of the following information(s) is/are sufficient?
(A) Chen spends Rs. 2000
(B) Brawn saves Rs. 700
(C) Brawn spends Rs. 5000
(a) Only A and B together are sufficient
(b) Only B and C together are sufficient
(c) A, B and C together are necessary
(d) Either A and B together or C alone sufficient
(e) Either A and B together or B and C together are sufficient
          
Q10. Manish and Satish were in partnership business for several years. At the end of 1997, a profit of Rs. 35000 was made by the two. To find out the share of Manish which of the following statements is/are sufficient?
A. Manish invested Rs. 35000 at the beginning of the year 1997.
B. Satish withdrew his capital at the end of the month of July.
C. Satish get 1/5 of his investment as share in profits.
(a) A and B together are sufficient
(b) B and C together are sufficient
(c) A and C together are sufficient
(d) All the three even together are not  sufficient
(e) All the three together are necessary

Q11. What is the total profit made in the business?
A. Hari and Vijay invested Rs. 20,000 and Rs. 30,000 respectively in a business. These are the only investors in business.
B. They decided 75% of their profit should be divided equally.
C. The remaining profit is divided in the ratio of investment.
(a) A alone is sufficient
(b) A and B together are sufficient
(c) A and C together are sufficient
(d) All are necessary
(e) All the three even together are not sufficient

Q12. D, K and A can do a work in 5, 15 and 35 days respectively. They get an amount of Rs. 1054 for finishing the work working together. What is the share of K in that amount?
(a) Rs. 242
(b) Rs. 324
(c) Rs. 238
(d) Rs. 245
(e) None of these

Q13. The ratio of the rate of flow of water in pipes varies inversely as the square of the radius of the pipes. What is the ratio of the rates of flow in two pipes of diameters 2 cm and 4 cm?
(a) 1:2
(b) 2:1
(c) 1:8
(d) 4:1
(e) None of these

Q14. Half the girls and one-third of the boys of a college reside in the hostel. What fractional part of the student body is hostelries if the total number of girls in the college in 100 and is ¼ of the total strength?
(a) 2/5
(b) 5/12
(c) 1/5
(d) 3/8
(e) 2/7

Q15. Given that 24 carat gold is pure gold; 18 carat gold is 3/4 gold and 20 carat gold is 5/6 gold, the ratio of the pure gold in 18 carat gold to the pure gold in 20 carat gold is
(a) 5:8
(b) 9:10
(c) 15:24
(d) 8:5
(e) 9:11

SOLUTIONS

 

Quantitative Aptitude

Directions (1-5): In each question, one or more equation(s) is (are) provided. On the basis of these, you have to find out relation between p and q

Solutions (1-5):

 
 
 
 

Directions (6-10): In each question, one or more equation(s) is (are) provided. On the basis of these, you have to find out relation between x and y

Solutions (6-10):

Q11. A certain number of tennis balls were purchased for Rs 450. Five more balls could have been purchased for the same amount if each ball was cheaper by Rs 15. Find the number of balls purchased.

(a) 10

(b) 16

(c) 25

(d) 18

(e) 45

Q12. The sum of the squares of two numbers is 170. The difference between thrice the smaller number and the larger number is 10. Find the numbers.   

(a) 7 and 12

(b) 7 and 10

(c) 8 and 11

(d)  7 and 11

(e) None of these

Q13. The length of a rectangular filed is seven times its breadth. If the area of the filed be 252 m2, find its length.   

(a) 40m

(b) 45m

(c) 42m

(d) 43m

(e) 46m

Q14. A packet food costs Rs. 360. If the quantity was 6 kg more and per kg costs Rs 3 less, the total cost would remain unchanged. How much the packet contains?  

(a) 21

(b) 31

(c) 29

(d) 25

(e) 24

Q15. A cyclist covers a distance of 24 km in a certain time with a certain fixed uniform speed. If he increases his speed by 2 km/hour, he takes 2 hr less to cover the same distance. Find his original speed.  

(a) 8

(b) 5.5

(c) 4

(d) 5

(e) 6

QUANT

Directions (1-15): What approximate value should replace the question mark (?) in the following equations:  

(a) 2

(b) 1

(c) 4

(d) 1/4

(e) None of these 

(a) 37.407

(b) 34.307

(c) 37.470

(d) 34.707

(e) 37.737

(a) -175500

(b) 165500

(c) 0

(d) -174500

(e) -140055 

(a) 2

(b) 1.08

(c) 0.076 

(d) 0.987

(e) 1

 

(a) 15

(b) 16

(c) 25

(d) 3/5

(e) 2 1/3

(a) 4.18

(b) 4.41

(c) 425

(d) 433

(e) None 

(a)  1400

(b) 1750

(c) 1350

(d) 1200

(e) 1650 

(a) 16

(b) 10

(c) 18

(d) 20

(e) 15 

(a) 5800

(b) 6300

(c) 6200

(d) 6500

(e) 6000

(a) 121

(b) 117

(c) 125

(d) 114

(e) 130

S10. Ans.(a)

Sol. 208×7.5% + 424×25% = 121

(a) 11,000

(b) 11,500

(c) 10,000

(d) 10,800

(e) 12,000

S11. Ans.(c)

Sol. ? = 10450 + 5585 – 5965 = 10070 = 10000

(a) 5500

(b) 6300

(c) 49000

(d) 4700

(e) 68000 

S12. Ans.(b)

Sol. ? = 1120 + 3015 + 2150 = 6285 = 6300

(a) 45

(b) 53

(c) 65

(d) 60

(e) 40

S13. Ans.(b)

Sol. ? = 121 – 68 = 53

(a) 160

(b) 150

(c) 145

(d) 170

(e) 130

S14. Ans.(c)

Sol. ? = 90 + 56 = 146 = 145

(a) 220

(b) 245

(c) 235

(d) 250

(e) 230 

S15. Ans.(e)

Sol. 256+40-68 = 228