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

Question : 16 [SSC CHSL 2010]

P can complete $1/4$ of a work in 10 days, Q can complete 40% of the same work in 15 days, R, completes $1/3$ of the work in 13 days and S, $1/6$ of the work in 7 days. Who will be able to complete the work first ?

a) Q

b) P

c) S

d) R

Answer: (a)

Time taken by P in completing 1 work

= 10 × 4 = 40 days

Time taken by Q in completing 1 work

= ${15 × 5}/2 = 75/2$ days

Time taken by R in completing 1 work

= 13 × 3 = 39 days

Time taken by S in completing 1 work

= 7 × 6 = 42 days

Clearly, Q took the least time i.e. $75/2$ or 37${1}/2$ days.

Question : 17 [SSC CGL Tier-1 2011]

A does half as much work as B in three- fourth of the time. If together they take 18 days to complete a work, how much time shall B take to do it alone?

a) 35 days

b) 30 days

c) 45 days

d) 40 days

Answer: (b)

Using Rule 2,

Let B completes the work in x days.

Work done by A in ${3x}/4$ days = $1/2$

Time taken by A in completing the work = $2 × {3x}/4 = {3x}/2$ days

(A + B)’s 1 day’s work

= $1/x + 2/{3x} = {3 + 2}/{3x} = 5/{3x}$

$5/{3x} = 1/18$ ⇒ 3x = 90 ⇒ x = 30

Hence, time taken by B in completing the work = 30 days

Question : 18 [SSC CGL Prelim 2007]

A contractor undertook to complete a project in 90 days and employed 60 men on it. After 60 days, he found that $3/4$ of the work has already been completed. How many men can he discharge so that the project may be completed exactly on time ?

a) 20

b) 40

c) 15

d) 30

Answer: (a)

Using Rule 1,

DaysWorkMen
60$3/4$60
30$1/4$x

∴ ${30 : 60}/{3/4 : 1/4}]$ : : 60 : x

$30 × 3/4 × x = 60 × 1/4 × 60$

$x = {60 × 60}/{30 × 3}$ = 40

Question : 19 [SSC CGL Tier-I 2016]

A, B and C contract a work for Rs. 440. A and B together are to do $9/11$ of the work. The share of C should be :

a) Rs. 90

b) Rs. 75

c) Rs. 80

d) Rs. 100

Answer: (c)

Work done by A and B together = $9/11$ parts

Work done by C = $1 - 9/11 = 2/11$ parts

Total amount = Rs. 440

∴ C’s share = Rs.$(2/11 × 440)$ = Rs.80

Question : 20 [SSC CGL Tier-I 2016]

A and B together can complete a work in 24 days. B alone does $1/3$ rd part of this work in 12 days. How many days will A alone take to complete the remaining work?

a) 36 days

b) 24 days

c) 72 days

d) 48 days

Answer: (d)

B completes $1/3$ work in 12 days.

B will complete 1 work in 12 × 3 = 36 days.

B’s 1 day’s work = $1/36$

(A + B)’s 1 day’s work = $1/24$

A’s 1 day’s work = $1/24 - 1/36$

= ${3 - 2}/72 = 1/72$

Time taken by A in doing 1work = 72 days

∴ Remaining work

= $1 - 1/3 = 2/3$

Time taken by A in doing $2/3$ work

= $2/3$ × 72 = 48 days

IMPORTANT quantitative aptitude EXERCISES

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