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

Answer: (d)

Time taken by B = $9 × 100/150$ = 6 days

Using Rule 17,

Here, x = 9, R = 50%

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

= $9 × 100/150$ = 6 days

Answer: (c)

Using Rule 2,

If Tapas alone takes x days to complete the work, then

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

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

$2x = 36 ⇒ x = 18$ days

Answer: (d)

Time taken by Sonia = 3x days (let)

Time taken by Pratibha = x days

3x - x = 60 ⇒ 2x = 60 ⇒ x = 30 days

Time taken by Sonia = 3x days

= 3 × 30 = 90 days.

Answer: (d)

Let B does the whole work in x days

Work done by B in 1 day = $1/x$

According to question

A does the $1/2$ work in $x/6$ days

A does the whole work in ${2x}/6 or = x/3$ days

Work done by A in one day = $3/x$

Work done by A and B together in one day

= $1/x + 3/x = 4/x$

Time taken to complete the whole work by A and B together

= $1/{4/x} = x/4$ days

Again, given that $x/4$ = 10 ∴ x = 40 days

Here, n = 3, d = 10

A is 3 times more efficient thanB.

Time taken by B = (n + 1) × D

= (3 + 1) × 10 = 40 days

Answer: (c)

Using Rule 2 and 3,

If B does the work in 3x days,

(A + C) will do the same work in x days.

If C does that work in 2y days.

(A + B) will do it in y days.

$1/x + 1/{3x} = 1/10$

$4/{3x} = 1/10$

$3x = 40 ⇒ x = 40/3$

Again, $1/y + 1/{2y} = 1/10$

$3/{2y} = 1/10 ⇒ y = 15$

(A + B + C)’s 1 day’s work = $1/10$

$1/A + 1/40 + 1/30 = 1/10$

$1/A = 1/10 - 1/40 - 1/30$

= ${12 - 3 - 4}/120 = 5/120 = 1/24$

A alone will complete the work in 24 days.