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

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

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: (c)

5m + 2w = 4m + 4w ⇒ m = 2w

Required ratio = 2 : 1

Answer: (d)

(A + B)’s 1 day’s work = $1/12$ ... (i)

(B + C)’s 1 day’s work = $1/15$ ... (ii)

Difference between A and C’s 1 day’s work

= $1/12 - 1/15 = {5 - 4}/60 = 1/60$

If A alone completes the work in x days, C will do the same in 2x days.

$1/x - 1/{2x} = 1/60$

${2 - 1}/{2x} = 1/60$

$1/{2x} = 1/60 ⇒ x = 30$

B’s 1 day’s work

= $1/12 - 1/30$ [From equation (i)]

= ${5 - 2}/60 = 3/60 = 1/20$

Hence, B alone will complete the work in 20 days.

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