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

Answer: (b)

Let the work be completed in x days.

According to the question,

${x - 5}/10 + {x - 3}/12 + x/15$ = 1

${6x - 30 + 5x - 15 + 4x}/60$ = 1

15x - 45 = 60

15x = 105 ⇒ x = $105/15$ = 7

Hence, the work will be completed in 7 days.

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: (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.

Answer: (a)

Let the work be completed in x days.

According to the question,

A worked for (x –3) days, while B worked for x days.

${x - 3}/9 +x/18$ = 1

${2x - 6 + x}/18$ = 1

3x–6 = 18

3x = 18 + 6 = 24 ⇒ x = $24/3$ = 8 days

Using Rule 8,

Here, x = 9, y = 18, m = 3

Total time taken = ${(x + m)y}/{x + y}$

=${(9 + 3) × 18}/{9 + 18}$

= ${12 × 18}/27$ = 8 days