Model 5  Split & Fraction of work Practice Questions Answers Test with Solutions & More Shortcuts

Question : 6 [SSC Constable (GD) 2012]

A can do $1/6$ of a work in 5 days and B can do $2/5$ of the work in 8 days. In how many days, can both A and B together do the work?

a) 13 days

b) 12 days

c) 20 days

d) 15 days

Answer: (b)

Using basics of Rule 2,

Time taken by A to finish the work

= 5 × 6 = 30 days

Time taken by B to complete the work

= ${8 × 5}/2$ = 20 days

(A + B)'s 1 day’s work

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

Required time = 12 days

Question : 7 [SSC CGL Tier-I 2010]

A can complete $1/3$ of a work in 5 days and B, $2/5$ of the work in 10 days. In how many days both A and B together can complete the work ?

a) 9$3/8$ days

b) 10 days

c) 7$1/2$ days

d) 8$4/5$ days

Answer: (a)

Using Rule 2,

Time taken by A alone in doing the work = 15 days

Time taken by B alone in doing the work

= ${10 × 5}/2$ = 25 days

(A + B)’s 1 day’s work

= $1/15 + 1/25 = {5 + 3}/75 = 8/75$

Hence, the work will be completed in $75/8 = 9{3}/8$ days.

Question : 8 [SSC MTS 2013]

A can do one and a half as much of a work which B can do in one day. B alone can do a piece of work in 18 days. They together can finish that work in

a) 11$1/5$ days

b) 10$1/5$ days

c) 7$1/5$ days

d) 5$1/5$ days

Answer: (c)

Using Rule 2,

Ratio of efficiency of A and B = 3 : 2

Ratio of time taken = 2 : 3

Time taken by A

= $2/3$ × 18 = 12 days

(A + B)’s 1 day’s work

= $1/12 + 1/18 = {3 + 2}/36 = 5/36$

Required time = $36/5 = 7{1}/5$ days

Question : 9 [SSC CGL Tier-II 2016]

John does $1/2$ piece of work in 3 hours, Joe does $1/4$ of the remaining work in 1 hour and George finishes remaining work in 5 hours. How long would it have taken the three working together to do the work ?

a) 3$1/7$ hours

b) 2$1/7$ hours

c) 2$8/11$ hours

d) 3$8/11$hours

Answer: (c)

According to the question,

John does $1/2$ work in 3 hours.

Time taken by John in doing whole work = 6 hours

Joe does $1/8$ work in 1 hour.

Time taken by Joe in doing whole work = 8 hours

Remaining work

= $1/2 - 1/8 = {4 - 1}/8 = 3/8$ parts

Time taken by George

= ${8 × 5}/3 = 40/3$ hours

Work done by all three in 1 hour

= $1/6 + 1/8 + 3/40$

= ${20 + 15 + 9}/120 = 44/120 = 11/30$

Required time = $30/11 = 2{8}/11$ hours

Question : 10 [SSC CGL Tier-I 2015]

A can do a work in 10 days and B in 20 days. If they together work on it for 5 days, then the fraction of the work that is left is

a) $4/3$

b) $3/4$

c) $1/4$

d) $3/20$

Answer: (c)

Using Rule 2

Work done by A and B in 1 day

= $1/10 + 1/20 = {2 + 1}/20 = 3/20$

(A + B)’s 5 days’ work

= ${5 × 3}/20 = 3/4$

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

IMPORTANT quantitative aptitude EXERCISES

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