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

Answer: (b)

A’s one day’s work = $1/6$

B’s one day’s work = $1/12$

(A + B)’s one day’s work = $1/6 + 1/12 = {2 + 1}/12 = 1/4$

(A + B)’s three day’s work = $3/4$

Remaining work = $1 - 3/4 = 1/4$

Total required number of days

= $1/4 × 12/1 + 3$ = 3 + 3 = 6 days

Using Rule 20,

Here, m = 6, n= 12, and p = 3

Time taken by B = $\text"mn - p(m+n)"/ \text"m"$

= ${6 × 12 - (6 + 12) × 3}/6 = {72 - 54}/6$ = 3 days

Total number of days taken to finish the works = 6 days

Answer: (b)

Time taken by A

= ${8 × 12}/128 = {8 × 12}/4 = 24$ days

Work done of by B = $4/12 = 1/3$

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

Since, A can complete a work in 24 days

A can complete $2/3$ part of work in 24 × $2/3$ = 16 days

Answer: (c)

(A+B)’s 2 days’ work = $2(1/12 + 1/18) = 10/36$

Remaining work = $1 - 10/36 = 26/36$

Time taken by B to complete $26/36$ part of work

= $26/36$ × 18 = 13 days

Using Rule 20,

Here, m = 12, n = 18, p = 2

Time taken by B = $\text"mn - p(m+n)"/ \text"m"$

= ${12 × 18 - 2(12 + 18)}/12$

= ${216 - 60}/12$ = 13 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: (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)

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