Model 3 Man leaves & joins Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

Let A worked for x days.

According to question

$x/28 + (x + 17)/35 = 1$

${5x + 4(x + 17)}/140 = 1$

5x + 4x + 68 = 140

9x = 140 - 68 = 72

x = 8

∴ A worked for 8 days

Answer: (d)

Suppose a man can complete the work in x days and that boys in y days.

According to question

$24/x + 24/y$ = 1 … (i) × 13

$26/x + 20/y = 1$ … (ii) × 12

$312/x + 312/y = 13$

$312/x + 240/y = 12$

Solving these two equations we get,

$72/y$ = 1 ⇒ y = 72 days

Boys alone can complete the work in 72 days

Here, a = 24, b = 24 - 6 = 18, d = 26 days

Total time taken by B alone to complete the work

= $\text"bd"/ \text"a - b"- 6$

(Since, man has work d or 6 days)

= ${18 × 26}/{24 - 18} - 6$ = 78 - 6 = 72 days

Answer: (b)

(B + C)’s 2 days’ work = $2(1/20 + 1/30)$

= $2({3 + 2}/60) = 1/6$ part

Remaining work = $1 - 1/6 = 5/6$ part

Time taken by A to complete this part of work

= $5/6$ × 18 = 15 days

Answer: (b)

Work done by 8 men in 6 days

= $6/12 = 1/2$

Remaining work

= $1 - 1/2 = 1/2$

4 more men are engaged.

Total number of men = 8 + 4 = 12

By work and time formula

$W_1/{M_1D_1} = W_2/{M_2D_2}$, we have

$1/{8 × 12} = {1/2}/{12 × D_2}$

$D_2 = 1/2 × {8 × 12}/12$ = 4 days.

Answer: (d)

Part of the work done by X in 8 days.

=$8/40 = 1/5$

[Since, work done in 1 day = $1/40$]

Remaining work = $1 - 1/5 = 4/5$

This part of work is done by Y in 16 days.

Time taken by Y in doing 1 work

= ${16 × 5}/4$ = 20 days

Work done by X and Y in 1 day

= $1/40 + 1/20 = {1+2}/40 = 3/40$

Hence, both together will complete the work in $40/3$

i.e.$13{1}/3$ days.

Answer: (a)

Since, A can finish the work in 18 days.

A’s one day’s' work = $1/18$

Similarly, B’s one day’s work = $1/24$

(A + B)’s 8 days’ work = $(1/18 + 1/24) × 8 = 7/72 × 8 = 7/9$

Remaining work = $1 - 7/9 = 2/9$

Time taken to finish the remaining work by B is $2/9 × 24 = 16/3 = 5{1}/3$ days

Here, m = 18, n= 24 and p = 8

Required Time = ${18 × 24 - 8(18 + 24)}/18$

= ${432 - 336}/18 = 96/18$

= $16/3 = 5{1}/3$ days