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

Answer: (b)

Using Rule 3,

Let time taken by A = x days

Time taken by B = 2x days

Time taken by C = 3x days

According to the question,

$1/x + 1/{2x} + 1/{3x}$ = 1 6

${6 + 3 + 2}/{6x} = 1/6$

$11/{6x} = 1/6$

6x = 6 × 11

$x = {6 × 11}/6$ = 11

Time taken by C alone = 3x = 3 × 11 = 33 days

Answer: (c)

Jyothi can do $3/4$ th of a job in 12 days.

Jyothi can do 1 job in ${12 × 4}/3$ = 16 days.

As Mala is twice as efficient as Jyothi,

Mala will finish the job in 8 days.

Answer: (c)

A does 20% less work than B.

Ratio of time taken = 5 : 4

A completes a work in $15/2$ hours

Time taken by B to do the same work

= $15/2 × 4/5$ = 6 hours.

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: (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: (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.