Model 5  Split & Fraction of work Section-Wise Topic Notes With Detailed Explanation And Example Questions

MOST IMPORTANT quantitative aptitude - 7 EXERCISES

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The following question based on time & work topic of quantitative aptitude

Questions : 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

The correct answers to the above question in:

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

Practice time & work (Model 5  Split & Fraction of work) Online Quiz

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Read more split and fraction of work Based Quantitative Aptitude Questions and Answers

Question : 1

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 : 2

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 : 3

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 : 4

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 : 5

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 : 6

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

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