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

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.

Answer: (c)

Using Rule 2,

If A completes the work in x days, B will take 2x days.

$1/x + 1/{2x} = 1/14 ⇒ {2 + 1}/{2x} = 1/14$

2x = 42 ⇒ x = 21 days

Answer: (a)

Using Rule 1,

Ratio of the working capabilities of a man, a woman and a child = 5 : 4 : 2

Ratio of man, woman and child equivalence = $1/5 : 1/4 : 1/2$

= $1/5 × 20 : 1/4 × 20 : 1/2 × 20$ = 4 : 5 : 10

or 4 men ≡ 5 women ≡ 10 children

4 men = 10 children

2 men ≡ 5 children and 6 men ≡ 15 children

5 women = 10 children

3 women ≡ 6 children

4 women ≡ 8 children

2 men + 3 women + 4 Children = 15 children

6 men + 4 women + 7 children = 30 children

∴ ${30 : 15}/{10 : 16}]$ : : 10 : x

where, x is no. of days

30 × 10 × x = 15 × 16 × 10

x = ${15 × 16 × 10}/{30 × 10} = 8$ 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: (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 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