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

Answer: (a)

Time taken by B in completing the work

=$12 × 100/160 = 15/2$ days

(A+B)’s 1 day’s work

= $1/12 + 2/15 = {5 + 8}/60 = 13/60$

Hence, the work will be completed in $60/13$ days

Using Rule 17,

Here, x = 12, R = 60%

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

= $12 × 100/160$ days = $15/2$ days

Now using Rule 2,

Time taken by A and B = ${xy}/{x + y}$

= ${12 × {15/2}}/{12 + {15/2}}$

= ${12 × 15}/39 = 60/13$ days

Answer: (d)

Using Rule 2,

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

$1/x + 1/{2x} = 1/12$

${2 + 1}/{2x} = 1/12 ⇒ 2x = 36$

B alone will complete the work in 36 days (i.e. 2x ).

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: (d)

Using Rule 2,

According to the question,

If A takes x days to complete the work, B will take 2x days and C will take 4x days,

Now, (A + B)'s 1 day’s work = $1/4$

$1/x + 1/{2x} = 1/4 ⇒ {2 + 1}/{2x} = 1/4$

2x = 12 ⇒ x = 6

C will complete the work in 4x i.e. 24 days.

Answer: (a)

Using Rule 2,

Time taken by A to complete the work = x days

Time taken by B to complete the work = 3x days

So, 3x - x = 2x = 40

x = 20 and 3x = 60

(A + B)’s 1 day’s work

= $1/20 + 1/60 = {3 + 1}/60 = 4/60 = 1/15$

A and B together will complete the work in 15 days.

Answer: (b)

Let B alone can do the work in x days.

A can do the work in ${3x}/2$ days.

According to the question,

$1/x + 2/{3x} = 1/18 ⇒ {3 + 2}/{3x} = 1/18$

$5/{3x} = 1/18 ⇒ 3x = 18 × 5$

$x = {18 × 5}/3$ = 30 days