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

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: (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: (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)

Work done by B in 9 days = $9/12 = 3/4$ part

Remaining work

= $1 - 3/4 = 1/4$ which is done by A

Time taken by A = $1/4 × 20$ = 5 days

Answer: (d)

(A + B)’s day’s work = $1/30$

(B + C)’s 1 day’s work = $1/24$

(C + A)’s 1 day’s work = $1/20$

2 (A + B + C)’s 1 day’s work = $1/30 + 1/24 + 1/20$

= ${4 + 5 + 6}/120 = = 15/120 = 1/8$

(A + B + C)’s 1 day’s work = $1/16$

(A + B + C)’s 10 days’ work = $10/16 = 5/8$

Remaining work = $1- 5/8 = 3/8$

This part of work is done by A alone.

Now A’s 1 day’s work = $1/16 - 1/24$

= ${3 - 2}/48 = 1/48$

The required no. of days

=$3/8 × 48$ = 18 days

Answer: (b)

Work done by 2 (A + B) in one day

= $1/10 + 1/15 = {3 + 2}/30 = 5/30 = 1/6$

Work done by (A + B) in one day = $1/12$

(A + B) can complete the work in 12 days