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

Answer: (c)

Let the work be finished in x days.

According to the question,

A worked for x days while B worked for (x - 3) days

$x/18 + {x - 3}/12 = 1$

${2x + 3x - 9}/36 = 1$

5x - 9 = 36

5x = 45 ⇒ x = $45/5$ = 9

Hence, the work was completed in 9 days.

Here, x = 18, y = 12, m = 3

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

= $({12 + 3}/{18 + 12})$ × 18 = 9 days

Answer: (c)

Work done by (A + C) in 2 days

= $2(1/10 + 1/20) = 2({2 + 1}/20) = 6/20 = 3/10$

Remaining work = $1 - 3/10 = 7/10$

(B + C)’s 1 day’s work

= $1/15 + 1/20 = {4 + 3}/60 = 7/60$

Time taken by (B + C) to finish $7/10$ part of the work

= $60/7 × 7/10$ = 6 days

Total time = 2 + 6 = 8 days

Answer: (a)

Since, A can finish the work in 18 days.

A’s one day’s' work = $1/18$

Similarly, B’s one day’s work = $1/24$

(A + B)’s 8 days’ work = $(1/18 + 1/24) × 8 = 7/72 × 8 = 7/9$

Remaining work = $1 - 7/9 = 2/9$

Time taken to finish the remaining work by B is $2/9 × 24 = 16/3 = 5{1}/3$ days

Here, m = 18, n= 24 and p = 8

Required Time = ${18 × 24 - 8(18 + 24)}/18$

= ${432 - 336}/18 = 96/18$

= $16/3 = 5{1}/3$ days

Answer: (b)

Part of work done by B in 10 days

= 10 × $1/15 = 2/3$

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

Time taken by A = $1/3 × 18$ = 6 days

Answer: (d)

Work done in first two days

= ${2/30 + 1/20 + 1/10 = 1/15 + 1/20 + 1/10$

= ${4 + 3 + 6}/60 = 13/60$

Work done in first 8 days = $52/60$

Remaining work

= $1 - 52/60 = 8/60 = 2/15$

(A + B)’s 1 day’s work

= $1/30 + 1/20 = {2 + 3}/60 = 1/12$

Remaining work = $2/15 - 1/12$

= ${8 - 5}/60 = 3/60 = 1/20$

(A + C)’s 1 day’s work

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

Time taken = $1/20 × 15/2 = 3/8$ day

Total time = $9 + 3/8 = 9{3}/8$ days

Answer: (d)

Let A and B worked together for x days

According to the question,

Part of work done by A for (x + 10) days

+ part of work done by B for x days = 1

${x + 10}/20 + x/30$ = 1

${3x + 30 + 2x}/60 = 1$

5x + 30 = 60

5x = 30 ⇒ x = $30/5$ = 6 days

Here, m =20, n= 30, p = x and time taken by A alone = 10

10 = ${mn - p(m + n)}/n$

10 = ${30 × 20 - x(30 + 20)}/30$

300 = 600 - x 50

50x = 300 x = 6

B worked for 6 days