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

Question : 21 [SSC CHSL 2015]

Janardan completes $2/3$ of his work in 10 days. Time he will take to complete $3/5$ of the same work, is

a) 6 days

b) 8 days

c) 4 days

d) 9 days

Answer: (d)

Using Rule 1,

${M_1D_1}/W_1= {M_2D_2}/W_2$

$10/{2/3} = D_2/{3/5}$

$30/2 = {5D_2}/3$

$D_2 = 30/2 × 3/5$ = 9 days

Question : 22 [SSC CGL Tier-II 2015]

Two workers A and B are engaged to do a piece of work. A working alone would take 8 hours more to complete the work than when work together. If B worked alone, would take 4$1/2$ hours more than when work together. The time required to finish the work together is

a) 4 hours

b) 5 hours

c) 6 hours

d) 8 hours

Answer: (c)

Time taken by A and B = x hours (let).

According to the question,

Time taken by A alone

= (x + 8) hours.

Time taken by B alone

= $(x + 9/2)$ hours.

$1/{x + 8} + 1/{x + {9/2}} = 1/x$

$1/{x + 8} + 2/{2x + 9} =1/x$

${2x + 9 + 2x + 16}/{(x + 8)(2x + 9)} = 1/x$

${4x + 25}/{2x^2 + 16x + 9x + 72} = 1/x$

$4x^2 + 25x = 2x^2 + 25x + 72$

$2x^2 = 72 ⇒ x^2 = 72/2 = 36$

x = $√{36}$ = 6 hours

Question : 23 [SSC CGL Prelim 2005]

A does $7/10$ part of work in 15 days. After that he completes the remaining work in 4 days with the help of B. In how many days will A and B together do the same work ?

a) 12$2/3$ days

b) 10$1/3$ days

c) 8$1/4$ days

d) 13$1/3$ days

Answer: (d)

Using Rule 2,

Remaining work = $1 - 7/10 = 3/10$

(A + B) take 4 days to do $3/10$ work

(A + B) will do the work in $4 × 10/3$ days

= $40/3 =13{1}/3$ days

Question : 24 [SSC CGL Tier-II 2015]

A company employed 200 workers to complete a certain work in 150 days. If only one fourth of the work has been done in 50 days, then in order to complete the whole work in time, the number of additional workers to be employed was

a) 300

b) 100

c) 200

d) 600

Answer: (b)

Using Rule 1,

200 workers do $1/4$ work in 50 days.

How many workers will do $3/4$ work in 100 days ?

Number of additional workers = x (let)

${M_1D_1}/W_1 = {M_2D_2}/W_2$

${200 × 50}/{1/4} = {(200 + x) × 100}/{3/4}$

(200 + x) 100 = 3 × 200 × 50

200 + x = 300

x = 300 - 200 = 100

Question : 25 [SSC CPO S.I.2003]

A can complete a work in 6 days while B can complete the same work in 12 days. If they work together and complete it, the portion of the work done by A is

a) $2/3$

b) $1/3$

c) $1/2$

d) $1/4$

Answer: (a)

Using Rule 2,

Time taken by A and B

= ${6 × 12}/{6 + 12} = {6 × 12}/18 = 4$

Work done by A in 4 days = $4/6 = 2/3$

IMPORTANT quantitative aptitude EXERCISES

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