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

Question : 26 [SSC CHSL 2012]

A alone can do a piece of work in 20 days and B alone in 30 days. They begin to work together. They will finish half of the work in :

a) 9 days

b) 8 days

c) 6 days

d) 12 days

Answer: (c)

(A+B)’s 1 day’s work

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

Work done in 6 days = $6/12 = 1/2$

Using Rule 2,

Here, x = 20, y = 30

They do the work in = ${xy}/{x + y}$ days

= ${20 × 30}/{20 + 30}$ = 12 days

Half of the work they do in 6 days

Question : 27 [SSC CGL Prelim 2008]

If 28 men complete $7/8$ of a piece of work in a week, then the number of men, who must be engaged to get the remaining work completed in another week, is

a) 6

b) 5

c) 3

d) 4

Answer: (d)

Using Rule1,

WorkDaysMen
$7/8$728
$1/8$7x

$7/8 : 1 8 : : 28 : x$

where x is no. of men

$7/8 × x = 1/8 × 28$

$x = {28 × 8}/{7 × 8}$ = 4

Question : 28 [SSC CHSL 2015]

A contractor was engaged to construct a road in 16 days. After working for 12 days with 20 labours it was found that only $5/8$th of the road had been constructed. To complete the work in stipulated time the number of extra labours required is :

a) 10

b) 18

c) 16

d) 12

Answer: (c)

Using Rule 1,

Remaining work

= $1 - 5/8 = 3/8$ ;

Remaining time = 4 days

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

${20 × 12}/{5/8} = {M_2 × 4}/{3/8}$

${20 × 12}/5 = {M_2 × 4}/3$

4 × 12 = ${M_2 × 4}/3$

$M_2$ = 12 × 3 = 36

Number of additional workers = 36 - 20 = 16

Question : 29 [SSC CAPFs SI, CISF ASI 2014]

A can do $7/8$ of work in 28 days, B can do $5/6$ of the same work in 20 days. The number of days they will take to complete if they do it together is

a) 17$3/5$ days

b) 15$3/7$ days

c) 13$5/7$ days

d) 14$5/7$ days

Answer: (c)

Using Rule 2,

A does $7/8$ work in 28 days.

A will complete the work in

$28 × 8/7$ = 32 days.

B does $5/6$ work in 20 days.

B will complete the work in

${20 × 6}/5$ = 24 days

(A + B)’s 1 day’s work

= $1/32 + 1/24 = {3 + 4}/96 = 7/96$

Required time = $96/7 =13{5}/7$ days

Question : 30 [SSC CPO SI 2016]

A and B work together to complete the rest of a job in 7 days. However, $37/100$ of the job was already done. Also, the work done by A in 5 days is equal to the work done by B in 4 days. How many days would be required by the fastest worker to complete the entire work?

a) 25

b) 20

c) 10

d) 30

Answer: (b)

Remaining work

= $1 - 37/100 = {100 - 37}/100 = 63/100$

Time taken by (A + B) in doing

$63/100$ part of work = 7 days

Time taken by them in doing whole work

= $100/63 × 7 = 100/9$ days

Respective ratio of time taken by

A and B in doing the work = 5 : 4

$1/{4x} + 1/{5x} = 9/100$

${5 + 4}/{20x} = 9/100$

20x = 100 ⇒ x = 5

Required time = 4 × 5 = 20 days

IMPORTANT quantitative aptitude EXERCISES

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