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

Answer: (a)

A is twice as good as B.

Time taken by A = x days

Time taken by B = 2x days

According to the question,

$1/x + 1/{2x} = 1/16$

${2 + 1}/{2x} = 1/16$

$3/x = 1/8$

x = 3 × 8 = 24 days

Answer: (d)

A : B = $D_2 : D_1$

100 : 140 = $D_2$ : 70

100 × 70 = 140 × $D_2$

$D_2 = {100 × 70}/140 = 50$ days.

Here, x = 70, r = 40%

Time taken by B = $x × 100/{100 + R}$

= ${70 × 100}/{100 + 40}$ = 50 days

Answer: (d)

Efficiency and time taken are inversely proportional Bimal : Kamal = 150 : 100 (work)

100 : 150 (Time) = 2 : 3

Since, 3 units ⇒ 15 days

2 units ⇒ $15/3 × 2$ = 10

Hence, Bimal complete the work in 10 days

Answer: (c)

5m + 2w = 4m + 4w ⇒ m = 2w

Required ratio = 2 : 1

Answer: (c)

According to the question,

1 man ≡ 2 boys

3 men + 4 boys ≡ (3 + 2) men ≡ 5 men

$M_1D_1 = M_2D_2$

5 × $D_1$ = 10 × 8

$D_1 = {10 × 8}/5$ = 16 days

Answer: (b)

Ratio of the work of A and B done in 1 day = 3 : 2

[Since, B's work doen = x (let), then A's work done = ${x + 50}/100 x = 3/2 x$ So, (A : B)'s work done = $3/2 x : x$ or 3 : 2 ]

Since, Work done by A and B together in 1 day = $1/15$

A’s 1 day’s work = $1/15 × 3/5= 1/25$

Hence, A alone will finish the work in 25 days.

Using Rule 22,

Here, n = $3/2$ because A is 50% more efficient than B.

D = 15

Time taken by A = $({n + 1}/n)$D days

= $({{3/2} + 1}/{3/2}) × 15$ = 25 days