Two persons K and L can complete a piece of work i | Time and Work Questions & Answers

Q:

Meghana alone would take 32 hours more to complete a job than both Meghana and Ganesh together. If Ganesh worked alone, he took 12 1/2 hours more to complete it than both Meghana and Ganesh worked together. What time would they take if both Meghana and Ganesh worked together?

A) 20 hrs	B) 18 hrs
C) 22 hrs	D) 20.5 hrs

Answer & Explanation Answer: A) 20 hrs

Explanation:

Time taken by both Meghana and Ganesh to work together is given by =

$\sqrt{t_{1} x t_{2}}$

Where

$t_{1} = 32 h r s t_{2} = 12 \frac{1}{2} h r s = \frac{25}{2} h r s$

Therefore, time took by both to work together =

$\sqrt{32 x \frac{25}{2}} = \sqrt{16 x 25} = 4 x 5 = 20 h r s$

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Q:

Aadi can do a piece of work in 12 days alone, Bunny can do the same work in 16 days alone. After Aadi has been working for 5 days and Bunny for 7 days, Charan finishes it in 14 days. In how many days will Charan alone be able to do the work?

A) 96 days	B) 48 days
C) 24 days	D) 12 days

Answer & Explanation Answer: A) 96 days

Explanation:

Let number of days Charan can do the same work alone is 'd' days.

According to the given data,

$\frac{5}{12} + \frac{7}{16} + \frac{14}{d} = 1 \frac{14}{d} = 1 - \frac{(20 + 21)}{48} \frac{14}{d} = \frac{48 - 41}{48} d = \frac{14 x 48}{7} d = 96 days$

Therefore, Charan alone can complete the work in 96 days.

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Q:

Prabhas is twice as good a workman as Rana and finishes a piece of work in 3 hours. In how many hours they together could finish that piece of work?

A) 3 hrs	B) 3.5 hrs
C) 2.5 hrs	D) 2 hrs

Answer & Explanation Answer: D) 2 hrs

Explanation:

Given Prabhas is twice as good a workman as Rana.

Prabhas finishes the work in 3 hrs

=> Rana finishes the work in 6 hrs.

Number of hours required together they could finish the work

= 3 x 6 / 3 + 6

= 18/9

= 2 hrs.

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Q:

Three athletes can complete one round around a circular field in 16, 24 and 36 min respectively. They start running together at same instant then after how much time they will meet to each other for first time ?

A) 2 hrs 24 min	B) 2 hrs 44 min
C) 1 hrs 24 min	D) 1 hrs 24 min

Answer & Explanation Answer: A) 2 hrs 24 min

Explanation:

Given that three athletes can complete one round around a circular field in 16, 24 and 36 min respectively.

Now, required time after which they met for the first time = LCM of (16, 24 & 36) min

Now, LCM of 16, 24, 36 = 144 minutes = 2 hrs 24 min.

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Q:

Raghu can do a job in 12 days alone and Sam can do the same job in 15 days alone. A third person Aru whose efficiency is two-third of efficiency of both Ram and Shyam together, can do the same job in how many days alone?

A) 10	B) 12
C) 13	D) 15

Answer & Explanation Answer: A) 10

Explanation:

One day work of Raghu and Sam together = 1/12 + 1/15 = 9/60 = 3/20

Aru efficiency = 2/3 of (Raghu + Sam)

Number of days required for Aru to do thw work alone = 3/2 x 20/3 = 10 days.

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Q:

12 men complete a work in 14 days. 5 days after they had started working, 3 men join them. How many more days will all of them take to complete the remaining work?

A) 5	B) 4
C) 3	D) 2

Answer & Explanation Answer: C) 3

Explanation:

Let p be the required number of days.

From the given data,

12 x 14 = 12 x 5 + (12+3) x p

12 x 14 = 12[5 + 3p]

14 = 5 + 3p

3p = 9

p = 3 days.

Hence, more 3 days all of them take to complete the remaining work.

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Q:

Lasya alone can do a work in 16 days. Srimukhi’s efficiency is 20 % lesser than that of Laya. If Rashmi and Srimukhi together can do the same work in 12 days, then find the efficiency ratio of Rashmi to that of Lasya?

A) 19 : 7	B) 30 : 19
C) 8 : 15	D) 31 : 17

Answer & Explanation Answer: C) 8 : 15

Explanation:

Given Lasya can do a work in 16 days.

Now, time taken by Srimukhi alone to complete the work = 16 x 100/80

Time taken by Rashmi = n days

=> (12 x 20)/(20 - 12) = (12 x 20)/n

=> n= 30 days.

Required ratio of efficiencies of Rashmi and Lasya = 1/30 :: 1/16 = 8 : 15.

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Q:

5 boys and 3 girls can together cultivate a 23 acre field in 4 days and 3 boys and 2 girls together can cultivate a 7 acre field in 2 days. How many girls will be needed together with 7 boys, if they cultivate 45 acres of field in 6 days?

A) 4	B) 3
C) 2	D) 1

Answer & Explanation Answer: C) 2

Explanation:

Let workdone 1 boy in 1 day be b

and that of 1 girl be g

From the given data,

4(5b + 3g) = 23

20b + 12g = 23 .......(a)

2(3b + 2g) = 7

6b + 4g = 7 ........(b)

Solving (a) & (b), we get

b = 1, g = 1/4

Let number og girls required be 'p'

6(7 x 1 + p x 1/4) = 45

=> p = 2.

Hence, number of girls required = 2

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A) 1/6	B) 1/3
C) 2/3	D) 1/18

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 ?

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