Model 3 Man leaves & joins Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

A’s 1 day’s work = $1/20$

A’s 4 days’ work = $4/20 = 1/5$

Remaining work = $1 - 1/5 = 4/5$

This part is completed by A and B together.

Now, (A + B)’s 1 day’s work = $1/20 + 1/12$

= ${3 + 5}/60 = 8/60 = 2/15$

Now, $2/15$ work is done by (A + B) in 1 day.

$4/5$ work is done in

= $15/2 × 4/5$ = 6 days.

Hence, the work lasted for 4 + 6 = 10 days.

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: (d)

Part of the work done by X in 8 days.

=$8/40 = 1/5$

[Since, work done in 1 day = $1/40$]

Remaining work = $1 - 1/5 = 4/5$

This part of work is done by Y in 16 days.

Time taken by Y in doing 1 work

= ${16 × 5}/4$ = 20 days

Work done by X and Y in 1 day

= $1/40 + 1/20 = {1+2}/40 = 3/40$

Hence, both together will complete the work in $40/3$

i.e.$13{1}/3$ days.