Model 6  Efficiency of the worker Section-Wise Topic Notes With Detailed Explanation And Example Questions

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

∴ ${30 : 15}/{10 : 16}]$ : : 10 : x

where, x is no. of days

30 × 10 × x = 15 × 16 × 10

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

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

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

Answer: (c)

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.

Answer: (d)

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

Here, n = 3, d = 10

A is 3 times more efficient thanB.

Time taken by B = (n + 1) × D

= (3 + 1) × 10 = 40 days

Answer: (d)

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.