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

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

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: (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

Answer: (b)

Work done by (A + B) in 1 day

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

(A + B)’s 2 days’ work = $2/6 = 1/3$

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

This part is done by A alone.

Since, one work is done by A in 15 days.

$2/3$ work is done in $15 × 2/3$ = 10 days.

Total number of days = 10 + 2 = 12 days

Using Rule 20,

Here, m = 15, n = 10, p =2

A alone completed the work in

= $\text"mn - p(m+n)"/ \text"n"$days

= ${15 × 10 - 2(15 + 10)}/10$

= ${150 - 50}/10$ = 10 days

Total time taken= 10 + 2 = 12 days