# Time and Work

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Time and Work:

Important Facts

• If A can do a piece of work in n days, then A’s 1 day’s work = 1/n
• If A’s 1 day’s work = 1/n, then A can finish the work in n days.
• If A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3:1
Ratio of times taken by A and B to finish a work = 1:3

# Aptitude Questions (Time and Work):

1. P can finish a work in 18 days and Q can do the same work in half the time taken by P. What part of the same work they can finish in a day if they working together?

A)    1/9

B)    1/6

C)    2/5

D)    2/7

E)    None of these

Explanation:

P’s 1 day’s work = 1/18 and Q’s 1 day’s work = 1/9
∴(P + Q)’s 1 day’s work = ((1/18)+(1/9))= 1/6

2. A, B, C can complete a piece of work in 24, 6 and 12 days respectively. In how much days they will complete the work if they work together:

A)    1/24 days

B)    7/24 days

C)    3(3/7) days

D)    4 days

E)    None of these

Explanation:

(A + B + C)’s 1 day’s work = (1/24+ 1/6+ 1/12)= 7/24
So, A, B and C together will complete the work in 24/7 = 3(3/7) days

3. A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. How much time will son, take to do it alone?

A)    6(1/2) days

B)    7 days

C)    7(1/2) days

D)    8 days

E)    None of these

Explanation:

Son’s 1 day’s work = (1/3-1/5)= 2/15
∴ The son alone can do the work in 15/2 = 7(1/2) days

4. P and Q can do a work in 12 days, Q and R in 15 days, R and P in 20 days. If they work together in how many days they will complete the work in?

A)    5 days

B)    7(5/6) days

C)    10 days

D)    15(2/3) days

E)    None of these

Explanation:

(P + Q)’s 1 day’s work = 1/12; (Q + R)’s 1 day’s work = 1/15; (P + R)’s 1 day’s work = 1/20
Adding, we get: 2(P + Q + R)’s 1 day’s work = (1/12+ 1/15+ 1/20) = 12/60 = 1/5
∴ (P + Q + R)’s 1 day’s work = 1/10
So, P, Q and R together can complete the work in 10 days.

5. P and Q can do a piece of work in 72 days; Q and R can do it in 120 days; P and R can do it in 90 days. In what time can P alone do it?

A)    120 days

B)    140 days

C)    170 days

D)    150 days

E)    None of these

Explanation:

(P + Q)’s 1 day’s work = 1/72; (Q + R)’s 1 day’s work = 1/120; (P + R)’s 1 day’s work = 1/90
Adding, we get: 2 (P + Q + R)’s 1 day’s work = (1/72+ 1/120+ 1/90)=12/360 = 1/30
(P + Q + R)’s 1 day’s work = 1/60
So, P’s 1 day’s work = (1/60-1/120)= 1/120
∴ P alone can do the work in 120 days.