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

Answer: (b)

Ratio of A's and B's efficiency = 4 : 5

Ratio of time taken = 5 : 4

Time taken by B = ${6 × 4}/5$

= $24/5 = 4{4}/5$ days

Using Rule 17,

Here, x = 6, R = 25%

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

= $6 × 100/125 = 6 × 4/5$

= $24/5 = 4{4}/5$ days

Answer: (b)

A is twice efficient than B.

Time taken by B = 12 days

Time taken by A = 6 days

(A + B)’s 1 day’s work

= $1/6 + 1/12 = {2 + 1}/12 = 1/4$

∴ Required time = 4 days

Answer: (c)

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

(A + B)’s 1 day’s work = $1/x + 1/{2x} = {2 + 1}/{2x} = 3/{2x}$

and C’s 1 day’s work = $3/{4x}$

$3/{4x} = 1/20$

4x = 3 × 20

$x = {3 × 20}/4 = 15$

(A + B + C)’s 1day’s work

= $1/{2x} + 1/x + 3/{4x} = 1/30 + 1/15 + 1/20$

= ${2 + 4 + 3}/60 = 9/60 = 3/20$

Hence, all three together will complete the work in

$20/3$ or $6{2}/3$ days.

Answer: (b)

Using Rule 2,

Let time taken by B in completing the work = x days

Time taken by A = (x - 10) days

⇒ $1/x + 1/{x - 10} = 1/12$

⇒ ${x - 10 + x}/{x(x - 10)} = 1/12$

⇒ $24x - 120 = x^2 - 10x$

⇒ $x^2 - 34x + 120$ = 0

⇒ $x^2 - 30x - 4x + 120$ = 0

⇒ $x (x - 30) - 4 (x - 30)$ = 0

⇒ $(x - 4) (x - 30)$ = 0

⇒ $x = 30$ because $x ≠ 4$

Answer: (b)

Using Rule 2,

Let time taken by P = x days

Then, time taken by Q = 3x days

3x - x = 48 ⇒ x = 24

(P + Q)’s 1 day’s work

= $1/24 + 1/72 = {3 + 1}/72 = 1/18$

Required time = 18 days