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

Question : 6 [SSC CGL Prelim 2003]

A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in :

a) 6 days

b) 10 days

c) 10$1/2$ days

d) 5 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.

Question : 7 [SSC CGL Prelim 2007]

A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in

a) 15$2/3$ days

b) 16$1/3$ days

c) 18$2/3$ days

d) 14$1/3$ 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.

Question : 8 [SSC DEO & LDC 2013]

A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the job ?

a) 60 days

b) 48 days

c) 54 days

d) 50 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.

Question : 9 [SSC MTS 2013]

A, B and C can complete a work in 10, 12 and 15 days respectively. They started the work together. But A left the work before 5 days of its completion. B also left the work 2 days after A left. In how many days was the work completed?

a) 5 days

b) 7 days

c) 8 days

d) 4 days

Answer: (b)

Let the work be completed in x days.

According to the question,

${x - 5}/10 + {x - 3}/12 + x/15$ = 1

${6x - 30 + 5x - 15 + 4x}/60$ = 1

15x - 45 = 60

15x = 105 ⇒ x = $105/15$ = 7

Hence, the work will be completed in 7 days.

Question : 10 [SSC CPO S.I.2004]

A and B can do a work in 45 days and 40 days respectively. They began the work together but A left after some time and B completed the remaining work in 23 days. After how many days of the start of the work did A leave ?

a) 9 days

b) 8 days

c) 5 days

d) 10 days

Answer: (a)

(A + B)’s 1 day’s work

= $(1/45 + 1/40) = {8 + 9}/360 = 17/360$

Work done by B in 23 days

= $1/40 × 23 = 23/40$

Remaining work = $1 - 23/40 = 17/40$

Now, $17/360$ work was done by (A + B) in 1 day

$17/40$ work was done by (A + B) in $1 × 360/17 × 17/40$ = 9 days.

Hence, A left after 9 days.

Using Rule 26
A and B can do a piece of work in x and y days, respectively. Both begin together but after some days.A leaves the job and B completed the remaining work in a days. After how many days did A leave?
Required time, t = $\text"(y - a)"/\text"(x + y)" × x$

Here, x = 45, y = 40, a = 23

Required time t= $\text"(y - a)"/\text"(x + y)" × x$

t = ${(40 - 23) × 45}/{45 + 40} = {17 × 45}/85$

t = 9 days

IMPORTANT quantitative aptitude EXERCISES

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