# Time and Work

Directions (Qs. 1 - 10): Study the following Questions carefully and choose the right answer:

1. 12 men and 15 women can do a piece of work in 24 days. In how many days can the work be done by 10 men and 12 women working together?

A) 12      B) 16      C) 18          D) Can't be determined           E) None of these

Explanation: The given information is not enough to answer the question.

Ans: D

2. 100 Men were employed to finish a work in 180 days. After 60 days it was found that only 1 ¾ of the work was done. How many more 5 men must be employed to finish the work in the stipulated time?

A) 100        B) 200            C) 300           D) 150           E) None of these

⇒  a = 200 ⇒ Total workers = 200

⇒  Extra men required = 200 − 100 = 100

Ans: A

3. If A can do 1/4 of a work in 3 days and B can do 1/6 of the same work in 4 days,how much will A get if both work together and are paid Rs.180 in all?

A) Rs.60             B) Rs.120        C) Rs.90           D) Rs.180             E) None of these

Explanation: A’s one day work =1/4 x 1/3 x =1/12

B’s one day work = 1/6 ×1/4 = 1/24

A’s wages: B’s wages

= A’s 1 day’s work : B’s 1 day’s work

= 1/12 : 1/24 = 2 : 1

⇒ A’s share = 2/3 × 180 = Rs.120

Ans: B

4. 20 women can complete a work in 14 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

A) 42/5            B) 56/5        C) 62/5      D) 34/5     E) None of these

Explanation: 20 women can complete the work in 14 days Let the work completed by 1 women in 1 day = w

So, work done by 20 women in 1 day = 20 × w

We know that work = M × D × H

Here,

M = no. of men, D = no. of days, H = hours

∴ Work done by 20 women in 14 days

= 20 × w × 14

Let the work completed by 1 child in 1 day = c

So, work completed by 10 children in 1 day

= 10 × c

So, work done by 10 children in 14 days

= 10 × c × 14

∴ Work is equal

∴ 20 × w × 14 = 10 × c × 14

2 × w = c

Let 5 women and 10 children complete the

work in = d days

∴ Complete work = (5 × w + 10 × c) × d

∴ 1 child = 2 women

∴10 children = 20 women

(5 women + 20 women) = 25 women

Again work is equal 25 × w × d = 20 × w × 14

So, d = 56/5 days

Ans: B

5. Anamika can do a piece of work in 30 days and Anjali can do the same work in 40 days. Anjali starts the work alone and works for 15 days and left the work. After that remaining work completed by Anamika and Arun together in 7 1/2 days. In how many days can 2 Arun do the whole work alone?

A) 15 days       B) 20 days           C) 30 days           D) 25 days         E) None of these

Explanation: Anamika's 1 day work = 1/30

Anjali's 1 day work =1/40

Anjali's 15 day work = 15/40 = 3/8

Remaining work = 1 − 3/8 = 5/8

Let Arun can do the work in 'm' days.

Arun's 1 day work = 1/40

According to the question,

m = 20 days

Arun can do the whole work in 20 days.

Ans: B

6. 10 men complete any work in 8 days and 16 women complete same work in 10 days. 8 women start the work and stop working after 4 days. How many men will complete the remaining work in 4 days?

A) 15 men         B) 20 men       C) 16 men        D) 12 men            E) None of these

Explanation: According to the question,

10m × 8 = 16w × 10

1m = 2w ⇒ 8 women = 4 men

Let ‘x’ men complete the remaining work in

4 days.

10 × 8 = (4 × 4) + (4 × x)

80 = 16 + 4x

4x = 64 ⇒ x = 16 men

Ans: C

7. Aman, Naman and Kamal can do a piece of work in 6 hours. Aman and Naman can do the same work in 8 hours and Naman and Kamal can do the same work in 12 hours. In how many times will Aman and Kamal do the same work?

A) 6 hours             B) 8 hours          C) 10 hours           D) 12 hours        E) 15 hours

Explanation: Let Aman and Kamal can do the same work in x hours. According to the question,

Ans: B

8. A can do a piece of work in 24 days, B is 20% more efficient than A. If C can do the work in 10 more days than B. In how many days can A and C do the whole work together?

A) 25 days           B) 35/2 days          C) 40/3  days           D) 18 days         E) None of these

Explanation: Ratio of the efficiency of A and B = 100 : 120 = 5 : 6

Ratio between the time taken by A and B = 6 : 5

If A can do the work in 24 days then B can do the same work in 24 / 6 × 5 = 20 days

C can do the same work in 20 + 10 = 30 days.

A and C together can do the same work

Ans:C

9. 6 men and 6 women together can complete a piece of work in 6 days. In how many days can 15 men alone complete the same work if 9 women alone can complete it in 10 days?

A) 5     B) 6     C) 7     D) Can't be determined       E) None of these

Explanation:

∴ 9 women can complete the work in 10 days

∴ 6 women can complete the work in

10 × 9 / 6 = 15 days

6 women in 6 days complete = 6 / 15 = 2 / 5 part

∴The remaining part (1 − 2 / 5 )= 3 / 5 part the will be completed by 6 men in 6 days

So, 6 men's work in 1 day = 3 / 5 x 6 = 1 / 10 part

∴ 6 men can complete the work in 10 days

∴ 15 men can complete the work in

6 × 10 /15 = 4 days

Ans: E

10. 4 goats or 6 sheeps can graze a field in 50 days. 2 goats and 9 sheeps can graze the field in.....

B) 100 days        B) 75 days           C) 50 days      D) 25 days           E) 45 days

Explanation: To solve this question, we can apply a short trick approach

Therefore, 2 goats = 3 sheeps

∴ 2 goats + 9 sheeps = 12 sheeps

Now, applying the chain rule formula, we get

M1D1 = M2D2

M1 = 6 sheeps, D1 = 50 days and M2 = 12

sheeps, D2 = ?

D2 = 6 x 50 / 12 = 25 days.

Ans: D

Posted Date : 27-07-2023

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