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

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: (a)

Time taken by Ramesh

= $4 × 2/3 = 8/3$ days

Work done by all three in 1 day

= $1/4 + 1/6 + 3/8 = {6 + 4 + 9}/24 = 19/24$

Required time

= $24/19 = 1{5}/19$ days

Answer: (d)

Ratio of efficiency of Babu and Asha

= 1 : $7/4$ = 4 : 7.

As the time taken is inversely proportional to efficiency, therefore, if Babu takes 7x days to complete work, Asha will take 4x days.

$1/{7x} + 1/{4x} = 1/7 ⇒ {4 + 7}/{28x} = 1/7$

28x = 11 × 7

$x = {11 × 7}/28 = 11/4$

Asha will complete the work in

$4x = 4 × 11/4$ = 11 days.

Using Rule 22,

Here, n = $7/4$, D = 7

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

= $({{7/4} + 1}/{7/4}) × 7 = 11/7 × 7$ = 11 days

Answer: (c)

Using Rule 2,

If A completes the work in x days,

B will do the same in 3x days.

3x - x = 60

2x = 60

x = 30 and 3x = 90

(A + B)’s 1 day’s work

= $1/30 + 1/90 = {3 + 1}/90$

= $4/90 = 2/45$

A and B together will do the work in $45/2$ or 22$1/2$ days.