Option 2 : 1500/13 days

Syllogism (Clear Your Basics)

67943

10 Questions
10 Marks
10 Mins

**Given:**

60 men or 75 boys can do a piece of work in 25 days

**Calculation:**

Let work done by 1 man in 1 day be m

And work done 1 boy in 1 day be n

According to the question:

Work done by 60 men in 1 day = 1/25

⇒ 60m = 1/25

⇒ m = 1/(25 × 60) = 1/1500

Again,

Work done by 75 boys = 1/25

⇒ 75n = 1/25

⇒ n = 1/(25 × 75) = 1/1875

Now, work done by 5 men and 10 boys take to complete the work in 1 day

⇒ 5 × (1/1500) + 10 × (1/1875)

⇒ (1/300) + (2/375)

⇒ (5 + 8)/1500

⇒ 13/1500

⇒ 13/1500

**∴ **The required time taken to complete the work is 1500/13 days

__Alternate Method__

60M = 75B

⇒ 4M = 5B

⇒ M : B = 5 : 4

Total work = (60 M × 25) units

⇒ (60 × 5 × 25) units

⇒ 7500 units

Total efficiency of 5 Men and 10 Boys = (5 × 5 + 10 × 4)

⇒ (25 + 40)

⇒ 65

Required time taken to complete the work = 7500/65

⇒ 1500/13

**∴ The required time taken to complete the work is 1500/13 days**