Time & Work Practice Set 2nd Solution Continues......

Solution of the Time & Work Practice Set Continues.................

Q29. 20 men can cut 30 trees in 4 hrs. If 4 men leave the job, how many trees will be cut in 12 hours?

(a) 72          (b) 80         (c) 68           (d) 79            (e) None of these.

Sol. Analyse the given data:-

M₁ = 20 men ,  W₁ = 30 trees,    H₁ = 4 hrs.   M₂ = 16 men,    H₂ = 12 hrs.,        W₂ = ?    

On applying Formula:-  M₁ × W₂ × H₁  = M₂ × W₁ × H₂.

20 × W₂ × 4 = 16 × 30 × 12.

W₂ = 72 trees.

Answer option (a).

Q30. A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it?

(a) 80 days            (b) 100 days              (c) 120 days            (d)150 days             (e) None of these

Sol. One day work details:

A + B → 1/72.                    .............................. eq.no. (i)

B + C → 1/120.                 ............................... eq.no.(ii)

A + C → 1/90.                   ............................... eq.no.(iii)

Eq.no. (i) + eq.no. (ii) + eq.no.(iii)

2(A + B + C) → 12/360.   

2(A + B + C) → 1/30.

A + B + C → 1/60.                ............................. eq.no.(iv)

Eq.no. (iv) – eq.no. (ii)

A → 1/60 – 1/120.

A → 1/120.  (One day work of “A”)

Hence A can complete the work in 120 days.

Answer option (c)

Q31. A and B together can complete a work in 6 days. They started together but after 4 days, B left the work. If the work is complete after 4 more days, A alone could do the work in how many days.

(a) 6                (b) 18            (c) 12              (d) 10         (e) None of these

Sol. Similar as Q.25

Answer option (b)

Q32. 90 men are engaged to do a piece of work in 40 days but it is found that in 25 days, 2/3 work is complete. How many men should be allowed to go off so that the work may be finished in time?

(a) 10             (b) 15         (c) 20        (d) 25         (e) None of these

Sol. Analyse the given data:-

M₁ = 90 men ,  D₁ = 25 days,  W₁ = 2/3 work.,  M₂ = ?, W₂ = 1/3 work, D₂ = 40 – 25 = 15 days    

On applying Formula:-  M₁ × D₁ × W₂  = M₂ × D₂ × W₁.

90 × 25 × (1/3) = M₂ × 15 × (2/3).

M₂ =  75 men. (required to complete the work on time).

Hence the no. of men go off the work = 90 – 75 = 15 men.

The required answer = 15 men.

Answer option (b).

Q33. 36 workmen are employed to finish a certain work in 48 days. But it is found that is 24 days only 2/5 work is done. How many more men must be taken to finish the work in time?

(a) 16            (b) 18     (c) 20         (d) 22    (e) None of these

Sol. Similar as Q32.

Answer option (b).

Q34. A and B together can complete a piece of work in 12 days, B and C can do it in 20 days and C and A can do it in 15 days. A, B and C together can complete it in?

(a) 12 days           (b) 8 days            (c) 6 days                (d) 10 days

Sol. Similar as Q22.

Answer option (d).

Q35. A and B together can complete a work in 3 days. They start together. But, after 2days, B left the work. If the work is completed after 2 more days, B alone could do the work in?

(a) 10 days         (b) 4.5 days         (c) 6 days             (d) 9 days    (e) None of these.

Sol. One day work detail:-

A + B → 1/3                               ......................... eq.no.(i)

Work done by A and B together in 2 days = 2/3 work.

Work remaining = 1/3 work.

According to question this remaining work is completed by A alone in 3 days.

“A” completes 1/3 work in 3 days.

Hence “A” alone completes this work in 9 days.

Now from eq.no.(i)

1/9 + B → 1/3

B → 1/3  - 1/9

B → 2/9   (one day work of “B”)

Hence B alone completes the work alone in 4.5 days.

Answer option (b).

Hope now you will be able to solve these type of questions in the competitive exams