CAT / #Quantitative Ability

October 25, 2017 @ 09:57 AM

October 25, 2017 @ 09:57 AM

K. J. Somaiya Institute of Management Studies and Research, Mumbai

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Time and Work

QA
Quantitative Ability – Time and Work

Question 1)

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C every third day?

A) 12 days

B) 15 days

C) 16 days

D) 18 days

Answer: Option B

Solution:

A’s 2 day’s work = (1/20*2) = 1/10

(A+B+C)’s 1 day’s work = (1/20 + 1/30 + 1/60) = 6/60 = 1/10

Work done in 3 days = (1/10 + 1/10) = 1/5

Now,1/5 work is done in 3 days

Whole work will be done in (3*5) = 15 days

Question 2)

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 ½ days

C) 25 days

D) 30 days

Answer: Option B

Solution:

Ratio of times taken by A and B = 1:3

The time difference is (3-1) 2 days while B takes 3 days and A takes 1 days

If difference of time is 2 days, B takes 3 days

If difference of time is 60days, B takes (3/2*60) = 90 days

So, A takes 30 days to do the work.

A’s 1 day’s work = 1/30

B’s day’s work = 1/90

(A+B)’s day’s work = (1/30 + 1/90) = 4/90 = 2/45

A and B together can do the work in 45/2 = 22 ½ days

Question 3)

A l=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

Answer: Option B

Solution:

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

Therefore, C’s share (for 3 days) = Rs. (3*1/24*3200) = Rs.400

Question 4)

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) 08 hours

B) 10 hours

C) 12 hours

D) 24 hours

Answer: Option C

Solution:

A’s 1 hour’s work = 1/4

(B+C)’s 1 hour’s work = 1/3

(A+B)’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

Question 5)

A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:

A) 15 days

B) 20 days

C) 25 days

D) 30 days

Answer: option C

Solution:

(A+ B)’s 1 day’s work = 1/10

C’s 1 day’s work = 1/50

(A + B+ C)’s 1 day’s work = (1/10 + 1/50) = 6/50 = 3/25……. (I)

A’s 1 day’s work = (B+C)’s 1 day’s work……(II)

From (I) and (II), we get: 2 * (A’s 1 day’s work) = 3/25

A’s 1 day’s work = 3/50

B’s day’s work (1/10 – 3/50) = 2/50 = 1/25

So, B alone could do the work in 25 days.

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