# Model 3 Man Leaves & Joins Practice Questions Answers Test With Solutions & More Shortcuts

#### TIME & WORK PRACTICE TEST [7 - EXERCISES]

Question : 1 [SSC CGL Prelim 2004]

A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days, B had to leave and A alone completed the remaining work. The whole work was completed in :

a) 8 days

b) 12 days

c) 15 days

d) 10 days

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

Question : 2 [SSC CPO S.I.2003]

A and B working separately can do a piece of work in 10 days and 15 days respectively. If they work on alternate days beginning with A, in how many days will the work be completed ?

a) 13 days

b) 12 days

c) 6 days

d) 18 days

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

Question : 3 [SSC CPO S.I.2003]

A and B can do a piece of work in 30 days while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work ?

a) 24 days

b) 30 days

c) 36 days

d) 18 days

(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

Question : 4 [SSC CHSL 2012]

A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in

a) 7 days

b) 11 days

c) 3 days

d) 5 days

Work done by B in 9 days = $9/12 = 3/4$ part

Remaining work

= $1 - 3/4 = 1/4$ which is done by A

Time taken by A = $1/4 × 20$ = 5 days

Question : 5 [SSC CPO S.I.2008]

A and B alone can complete work in 9 days and18 days respectively. They worked together; however 3 days before the completion of the work A left. In how many days was the work completed ?

a) 8 days

b) 6 days

c) 5 days

d) 13 days

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

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