Time and Work Questions

FACTS  AND  FORMULAE  FOR  TIME  AND  WORK  QUESTIONS

 

 

1. If A can do a piece of work in n days, then A's 1 day's work =1n

2. If A’s 1 day's work =1n, then A can finish the work in n days.

 

3. 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.

 

NOTE : 

Efficiency1No of time units

 

 Efficiency × Time = Constant Work

 

Hence, Required time = WorkEfficiency

 

Whole work is always considered as 1, in terms of fraction and 100% , in terms of percentage.

In general, number of day's or hours = 100Efficiency

Q:

Pavan and Sravan are two persons. If Pavan works with his actual efficiency and Sravan twice of his actual efficiency then it takes 25 days to complete the work. But If Pavan works twice of his actual efficiency and Sravan with his normal efficiency then the work is completed in 20 days. How many days would it take if Sravan alone works with his actual efficiency (in Days)?

A) 50 B) 100
C) 70 D) 35
 
Answer & Explanation Answer: B) 100

Explanation:

Let the Efficiency of pavan be E(P)

Let the Efficiency of sravan be E(S)

Here Work W = LCM(25,20) = 100

Now, E(P+2S) = 100/25 = 4 ....(1)

E(2P+S) = 100/20 = 5 ....(2)

Hence, from (1) & (2) we get

E(S) = 1

=> Number of days Savan alone work to complete the work  = 100/1 = 100 days.

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10 4495
Q:

A work which could be finished in 11 days was finished 4 days earlier after 4 more men joined. The number of men employed was ?

A) 7 B) 8
C) 9 D) 10
 
Answer & Explanation Answer: A) 7

Explanation:

As the work is same
M1D1 = M2D2

Here Let the number of men employed was M
=> 11M = 7(M+4)
=> 11M - 7M = 28
=> M = 7

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4 4351
Q:

Two persons K and L can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 3 days ?

A) 1/6 B) 1/3
C) 2/3 D) 1/18
 
Answer & Explanation Answer: A) 1/6

Explanation:

K's one day's work = 1/30
L's one day's work = 1/45
(K + L)'s one day's work = 1/30 + 1/45 = 1/18

The part of the work completed in 3 days = 3 (1/18) = 1/6.

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5 4307
Q:

10 boys can complete a work in 7 days and 10 girls take 14 days to complete the work. How many days will 5 boys and 10 girls take to complete the work ?

A) 13 days B) 10 days
C) 7 days D) 16 days
 
Answer & Explanation Answer: C) 7 days

Explanation:

1 boy's 1 day work = 1/70

1 girl's 1 day work = 1/140

(5 boys + 10 girls)'s 1 day work = (5/70 + 10/140) = (1/14 + 1/14) = 1/7

 

5 boys and 10 girls will complete the work in 7 days.

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2 4246
Q:

K is 4 times as fast as L and working together, they can complete a work in 24 days. In how many days can L alone complete the work ?

A) 30 days B) 40 days
C) 120 days D) 80 days
 
Answer & Explanation Answer: A) 30 days

Explanation:

Given K=4L 

-->K+L = 4L+L = 5L

 

These 5L people can complete the work in 24 days, which means L alone can do the work in (24 x 5)=120 days.

 

Hence, K alone can do the work in 120/4= 30 days.

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4 4237
Q:

A and B can do a piece of work for Rs 1540. Find the difference between the wages of C and B for the same work If A can do the work in 12 days and B can do the same work in 8 days and with the help of C, A and B can do the same work in 2 days?

A) 980 B) 1232
C) 810 D) 1121
 
Answer & Explanation Answer: B) 1232

Explanation:

From the given data,


                       Day      Capacity

A              ->    12          2

B              ->     8           3             2

A + B + C ->     2            12

=> Capacity of C = 12 - 5 = 7

Ratio of capacity of A : B : C = 2 : 3 : 7

Difference of wages of C & B = 4/5 x 1540

= 4 x 308 = Rs. 1232

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13 4219
Q:

10 women can do a piece of work in 6 days, 6 men can do same work in 5 days and 8 children can do it in 10 days. What is the ratio of the efficiency of a woman, a man and a child respectively?

A) 4 : 6 : 3 B) 4 : 5 : 3
C) 2 : 4 : 3 D) 4 : 8 : 3
 
Answer & Explanation Answer: D) 4 : 8 : 3

Explanation:
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4 4217
Q:

Priya can do a work in 16 days. In how many days will the work be completed by Sai, if the efficiency of Sai is 60% more than that of Priya ?

A) 8 days B) 12 days
C) 14 days D) 10 days
 
Answer & Explanation Answer: D) 10 days

Explanation:

Ratio of efficiencies of Priya and Sai is

Sai : Priya = 160 : 100 = 8 : 5

Given Priya completes the work in 16 days

Let number of days Sai completes the work be 'd'

=> 5×16 = 8×d

d = 10 days.

Therefore, number of days Sai completes the work is 10 days.

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13 4153