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

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: (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: (b)

Time taken by B

= $12 × 100/160 = 15/2 = 7{1}/2$ 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 = 7$1/2$ days

Answer: (c)

Using Rule 2,

Time taken by B

= $130/100 × 23 = 299/10$ days

(A + B)’s 1 day’s work

= $1/23 + 10/299$

= ${13 + 10}/299 = 23/299 = 1/13$

Time taken by (A + B) = 13 days

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: (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 $x ≠ 20/9$