Practice Split and fraction of work - quantitative aptitude Online Quiz (set-1) For All Competitive Exams

Q-1)   If 12 men working 8 hours a day complete the work in 10 days, how long would 16 men working 7$1/2$ hours a day take to complete the same work?

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

MenWorking hoursDays
12810
167$1/2$x

∴ ${16 : 12}/{15/2 : 8}]$ : : 10 : x

16 × $15/2$ × x = 12 × 8 × 10

8 × 15 × x = 12 × 8 × 10

$x = {12 × 8 × 10}/{8 × 15}$ = 8 days


Q-2)   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)

(b)

(c)

(d)

Explanation:

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.


Q-3)   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)

(b)

(c)

(d)

Explanation:

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


Q-4)   P can do $(1/4)$th of work in 10 days, Q can do 40% of work in 40 days and R can do $(1/3)$rd of work in 13 days. Who will complete the work first?

(a)

(b)

(c)

(d)

Explanation:

Since, P does $1/4$ th work in 10 days.

P will do 1 work in 10 × 4 = 40 days

Since, Q, does 40% part of work in 40 days

Q will do 100% work in

${40 × 100}/40$ = 100 days

Since, R, does $1/3$ rd work in 13 days.

R will do 1 work in 13 × 3 = 39 days


Q-5)   A can complete $2/3$ of a work in 4 days and B can complete $3/5$ of the work in 6 days. In how many days can both A and B together complete the work ?

(a)

(b)

(c)

(d)

Explanation:

Using basics of Rule 2,

Time taken by A to complete the work

= ${4 × 3}/2$ = 6 days

Time taken by B to complete the work

= ${6 × 5}/3$ = 10 days

(A + B)’s 1 day’s work

= $1/6 + 1/10 = {5 + 3}/30 = 8/30 = 4/15$

A and B together will complete the work in

$15/4 = 3{3}/4$ days.


Q-6)   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)

(b)

(c)

(d)

Explanation:

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


Q-7)   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)

(b)

(c)

(d)

Explanation:

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


Q-8)   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)

(b)

(c)

(d)

Explanation:

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


Q-9)   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)

(b)

(c)

(d)

Explanation:

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


Q-10)   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)

(b)

(c)

(d)

Explanation:

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 = $1 - 3/4 = 1/4$