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

Answer: (a)

(A + B)’s 1 day’s work

= $(1/45 + 1/40) = {8 + 9}/360 = 17/360$

Work done by B in 23 days

= $1/40 × 23 = 23/40$

Remaining work = $1 - 23/40 = 17/40$

Now, $17/360$ work was done by (A + B) in 1 day

$17/40$ work was done by (A + B) in $1 × 360/17 × 17/40$ = 9 days.

Hence, A left after 9 days.

Here, x = 45, y = 40, a = 23

Required time t= $\text"(y - a)"/\text"(x + y)" × x$

t = ${(40 - 23) × 45}/{45 + 40} = {17 × 45}/85$

t = 9 days

Answer: (b)

Part of the work done by A and B in 4 days

= $4(1/12 + 1/15) = 4({5 + 4}/60)$

= $4 × 9/60 = 3/5$

Remaining work = $1 - 3/5 = 2/5$

Time taken by B to complete the remaining work

= $2/5 × 15$ = 6 days

Using Rule 20,

Here, m = 12, n = 15, p = 4

B alone do the works in= ${mn - p(m + n)}/m$

= ${12 × 15 - 4(12 + 15)}/12$

= ${180 - 108}/12 = 72/12$ = 6 days

Answer: (c)

B’s 1 day's work

= $1/12 - 1/20 = {5 - 3}/60 = 1/30$

B's $1/2$ day’s work = $1/60$

(A + B)'s 1 day's work

= $1/20 + 1/60 = {3 + 1}/60 = 1/15$

[Since, B works for half day daily]

Hence, the work will be completed in 15 days.

Answer: (a)

(A+B)’s 1 day’s work = $1/30$

(A + B)’s 20 day’s work = $20/30 = 2/3$

Remaining work = $1 - 2/3 = 1/3$

Now, $1/3$ part of work is done by A in 20 days.

Whole work will be done by A alone in 20 × 3 = 60 days.

Answer: (d)

A’s 1 day’s work = $1/12$

B’s 1 day’s work = $1/18$

Part of work done by A and B in first two days

= $1/12 + 1/18 = {3 - 2}/36 = 5/36$

Part of work done by A and B in 14 days = $35/36$

[14 days to be taken randomly]

Remaining work = $1 - 35/36 = 1/36$

Now A will work for 15th day.

A will do the $1/36$ work in $1/36 × 12 = 1/3$ day.

Total Work will be done in $14{1}/3$ days.

Answer: (b)

Work done by (B + C) in 3 days.

= $3 × (1/9 + 1/12)$

= $1/3 + 1/4 = {4 + 3}/12 = 7/12$

Remaining work = $1 - 7/12 = 5/12$

This part of work is done by A alone.

Now, $1/24$ part of work is done by A in 1 day.

∴ $5/12$ part of work will be done by A in

= $24 × 5/12$ = 10 days.