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

Question : 6 [SSC MTS 2011]

A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work is

a) 42 days

b) 11 days

c) 21 days

d) 28 days

Answer: (c)

Using Rule 2,

If A completes the work in x days, B will take 2x days.

$1/x + 1/{2x} = 1/14 ⇒ {2 + 1}/{2x} = 1/14$

2x = 42 ⇒ x = 21 days

Question : 7 [SSC CPO S.I.2008]

A 10 hectare field is reaped by 2 men, 3 women and 4 children together in 10 days. If working capabilities of a man, a woman and a child are in the ratio 5 : 4 : 2, then a 16 hectare field will be reaped by 6 men,4 women and 7 children in

a) 8 days

b) 5 days

c) 6 days

d) 7 days

Answer: (a)

Using Rule 1,

Ratio of the working capabilities of a man, a woman and a child = 5 : 4 : 2

Ratio of man, woman and child equivalence = $1/5 : 1/4 : 1/2$

= $1/5 × 20 : 1/4 × 20 : 1/2 × 20$ = 4 : 5 : 10

or 4 men ≡ 5 women ≡ 10 children

4 men = 10 children

2 men ≡ 5 children and 6 men ≡ 15 children

5 women = 10 children

3 women ≡ 6 children

4 women ≡ 8 children

2 men + 3 women + 4 Children = 15 children

6 men + 4 women + 7 children = 30 children

ChildrenFieldDays
151010
3016x

∴ ${30 : 15}/{10 : 16}]$ : : 10 : x

where, x is no. of days

30 × 10 × x = 15 × 16 × 10

x = ${15 × 16 × 10}/{30 × 10} = 8$ days

Question : 8 [SSC CGL Tier-II 2013]

Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked $1/3$ as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require

a) 8$3/4$ days

b) 5$1/5$ days

c) 6$1/4$ days

d) 7$1/2$ days

Answer: (c)

Using Rule 2,

If A alone does the work in x days and B alone does the work in y days, then

$1/x + 1/y = 1/5$ ...(i)

Again, $2/x + 1/{3y} = 1/3$ ...(ii)

By equation (ii) × 3 - (i),

$6/x + 1/y - 1/x - 1/y = 1 - 1/5$

$6/x - 1/x = 4/5$

${6 - 1}/x = 4/5$

$x = 25/4 = 6{1}/4$ days

Question : 9 [SSC CGL Tier-I 2015]

If A, B and C can complete a work in 6 days. If A can work twice faster than B and thrice faster than C, then the number of days C alone can complete the work is :

a) 11 days

b) 33 days

c) 44 days

d) 22 days

Answer: (b)

Using Rule 3,

Let time taken by A = x days

Time taken by B = 2x days

Time taken by C = 3x days

According to the question,

$1/x + 1/{2x} + 1/{3x}$ = 1 6

${6 + 3 + 2}/{6x} = 1/6$

$11/{6x} = 1/6$

6x = 6 × 11

$x = {6 × 11}/6$ = 11

Time taken by C alone = 3x = 3 × 11 = 33 days

Question : 10 [SSC CPO S.I.2009]

Jyothi can do $3/4$ of a job in 12 days. Mala is twice as efficient as Jyothi. In how many days will Mala finish the job ?

a) 16 days

b) 6 days

c) 8 days

d) 12 days

Answer: (c)

Using Rule 1
If $M_1$ men can finish $W_1$ work in $D_1$ days and $M_2$ men can finish $W_2$ work in $D_2$ days then, Relation is
${M_1D_1}/{W_1} = {M_2D_2}/{W_2}$ and
If $M_1$ men finish $W_1$ work in $D_1$ days, working $T_1$ time each day and $M_2$ men finish $W_2$ work in $D_2$ days, working $T_2$ time each day, then
${M_1D_1T_1}/{W_1} = {M_2D_2T_2}/{W_2}$

Jyothi can do $3/4$ th of a job in 12 days.

Jyothi can do 1 job in ${12 × 4}/3$ = 16 days.

As Mala is twice as efficient as Jyothi,

Mala will finish the job in 8 days.

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