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

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: (d)

Using Rule 2,

If the time taken by B to complete the work be x days,

then time taken by A = (x - 5) days

$1/x + 1/{x - 5} = 9/100$

⇒ ${x - 5 + x}/{x(x - 5)} = 9/100$

⇒ $9x^2 - 45x = 200x –500$

⇒ $9x^2 - 245x + 500 = 0$

⇒ $9x^2 - 225x - 20x + 500 = 0$

⇒ $9x (x - 25) - 20 (x - 25)$ = 0

⇒ $(x - 25) (9x - 20)$ = 0

⇒ $x = 25$ because $x ≠ 20/9$

Answer: (c)

Time taken by Shashi in doing 1 work = 20 days

Tanya is 25% more efficient than Shashi.

Time taken by Tanya

= $100/125 × 20$ = 16 days

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)

Using Rule 2,

If A alone does the work in x days and B alone does the work in y days, then

$1/x + 1/y = 1/5$ ...(i)

Again, $2/x + 1/{3y} = 1/3$ ...(ii)

By equation (ii) × 3 - (i),

$6/x + 1/y - 1/x - 1/y = 1 - 1/5$

$6/x - 1/x = 4/5$

${6 - 1}/x = 4/5$

$x = 25/4 = 6{1}/4$ 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