# Model 6  Efficiency Of The Worker Practice Questions Answers Test With Solutions & More Shortcuts

#### TIME & WORK PRACTICE TEST [7 - EXERCISES]

Question : 1 [SSC CHSL 2011]

A can do a work in 9 days, if B is 50% more efficient than A, then in how many days can B do the same work?

a) 3 days

b) 13.5 days

c) 4.5 days

d) 6 days

Time taken by B = \$9 × 100/150\$ = 6 days

Using Rule 17,

Here, x = 9, R = 50%

Time taken by B = \$x × 100/{100 + R}\$ days

= \$9 × 100/150\$ = 6 days

Question : 2 [SSC CPO S.I.2010]

Tapas works twice as fast as Mihir. If both of them together complete a work in 12 days, Tapas alone can complete it in

a) 24 days

b) 15 days

c) 18 days

d) 20 days

Using Rule 2,

If Tapas alone takes x days to complete the work, then

\$1/x + 1/{2x} = 1/12\$

\${2 + 1}/{2x} = 1/12\$

\$2x = 36 ⇒ x = 18\$ days

Question : 3 [SSC CGL Tier-I 2014]

Pratibha is thrices as efficient as Sonia and is therefore able to finish a piece of work in 60 days less than Sonia. Pratibha and Sonia can individually complete the work respectively in

a) 40 days, 120 days

b) 30 days, 60 days

c) 60 days, 90 days

d) 30 days, 90 days

Time taken by Sonia = 3x days (let)

Time taken by Pratibha = x days

3x - x = 60 ⇒ 2x = 60 ⇒ x = 30 days

Time taken by Sonia = 3x days

= 3 × 30 = 90 days.

Question : 4 [SSC CGL Prelim 2005]

A does half as much work as B in one sixth of the time. If together they take 10 days to complete a work, how much time shall B take to do it alone?

a) 50 days

b) 70 days

c) 30 days

d) 40 days

Let B does the whole work in x days

Work done by B in 1 day = \$1/x\$

According to question

A does the \$1/2\$ work in \$x/6\$ days

A does the whole work in \${2x}/6 or = x/3\$ days

Work done by A in one day = \$3/x\$

Work done by A and B together in one day

= \$1/x + 3/x = 4/x\$

Time taken to complete the whole work by A and B together

= \$1/{4/x} = x/4\$ days

Again, given that \$x/4\$ = 10 ∴ x = 40 days

Using Rule 22
The efficiency of A to work is 'n' times more than that of B, Both start to work together and finish it in 'D' days. Then, A and B will separately complete, the work in \$({n + 1}/n)\$D and (n + 1) D days respectively.

Here, n = 3, d = 10

A is 3 times more efficient thanB.

Time taken by B = (n + 1) × D

= (3 + 1) × 10 = 40 days

Question : 5 [SSC Delhi Police S.I.2012]

To do a certain work, B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. The time taken by A to complete the work separately is

a) 20 days

b) 22 days

c) 24 days

d) 30 days

Using Rule 2 and 3,

If B does the work in 3x days,

(A + C) will do the same work in x days.

If C does that work in 2y days.

(A + B) will do it in y days.

\$1/x + 1/{3x} = 1/10\$

\$4/{3x} = 1/10\$

\$3x = 40 ⇒ x = 40/3\$

Again, \$1/y + 1/{2y} = 1/10\$

\$3/{2y} = 1/10 ⇒ y = 15\$

(A + B + C)’s 1 day’s work = \$1/10\$

\$1/A + 1/40 + 1/30 = 1/10\$

\$1/A = 1/10 - 1/40 - 1/30\$

= \${12 - 3 - 4}/120 = 5/120 = 1/24\$

A alone will complete the work in 24 days.

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