Model 6  Efficiency of the worker Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11 [SSC GL Tier-I 2013]

A does 20% less work than B. If A can complete a piece of work in 7$1/2$ hours, then B can do it in

a) 5 hours

b) 6$1/2$ hours

c) 6 hours

d) 5$1/2$ hours

Answer: (c)

A does 20% less work than B.

Ratio of time taken = 5 : 4

A completes a work in $15/2$ hours

Time taken by B to do the same work

= $15/2 × 4/5$ = 6 hours.

Question : 12 [SSC CHSL 2011]

A can do a work in 5 days less than the time taken by B to do it. If both of them together take11$1/9$ days, then the time taken by ‘B’ alone to do the same work (in days) is

a) 30

b) 15

c) 20

d) 25

Answer: (d)

Using Rule 2,

If the time taken by B to complete the work be x days,

then time taken by A = (x - 5) days

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

⇒ ${x - 5 + x}/{x(x - 5)} = 9/100$

⇒ $9x^2 - 45x = 200x –500$

⇒ $9x^2 - 245x + 500 = 0$

⇒ $9x^2 - 225x - 20x + 500 = 0$

⇒ $9x (x - 25) - 20 (x - 25)$ = 0

⇒ $(x - 25) (9x - 20)$ = 0

⇒ $x = 25$ because $x ≠ 20/9$

Question : 13 [SSC CGL Tier-I 2016]

Shashi can do a piece of work in 20 days. Tanya is 25% more efficient than Shashi. The number of days taken by Tanya to do the same piece of work is :

a) 25

b) 15

c) 16

d) 18

Answer: (c)

Time taken by Shashi in doing 1 work = 20 days

Tanya is 25% more efficient than Shashi.

Time taken by Tanya

= $100/125 × 20$ = 16 days

Question : 14 [SSC CHSL 2011]

A is 30% more efficient than B, and can alone do a work in 23 days. The number of days, in which A and B, working together can finish the job is

a) 21 days

b) 11 days

c) 13 days

d) 20 days

Answer: (c)

Using Rule 2,

Time taken by B

= $130/100 × 23 = 299/10$ days

(A + B)’s 1 day’s work

= $1/23 + 10/299$

= ${13 + 10}/299 = 23/299 = 1/13$

Time taken by (A + B) = 13 days

Question : 15 [SSC CGL Prelim 2007]

To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it ?

a) 45 days

b) 30 days

c) 35 days

d) 40 days

Answer: (b)

Using Rule 2
If A completes a piece of work in 'x' days, and B completes the same work in 'y' days, then,
Work done by A in 1 day = $1/x$, Work done by B in 1 day = $1/y$
Work done by A and B in 1 day = $1/x + 1/y = {x + y}/{xy}$
Total time taken to complete the work by A and B both = $({xy}/{x + y})$

Let B alone can do the work in x days.

A can do the work in ${3x}/2$ days.

According to the question,

$1/x + 2/{3x} = 1/18 ⇒ {3 + 2}/{3x} = 1/18$

$5/{3x} = 1/18 ⇒ 3x = 18 × 5$

$x = {18 × 5}/3$ = 30 days

IMPORTANT quantitative aptitude EXERCISES

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