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A group of workers including 10 men and 5 women can finish certain amount of work in 25 days. If the women in the group are replaced by men, then the work can be finished 5 days earlier. The wages are Rs 500/day for men and Rs 400/day for women. How much does it cost when 13 men and 7 women finished the entire work?

A group of workers including 10 men and 5 women can finish certain amount of work in 25 days. If the women in the group are replaced by men, then the work can be finished 5 days earlier. The wages are Rs 500/day for men and Rs 400/day for women. How much does it cost when 13 men and 7 women finished the entire work? Correct Answer Rs. 176700

Let the total amount of work be X.

If the women are replaced by men, the group now has 15 men.

Number of days taken by 15 men to finish the work = 20 days

Work done by 15 men in one day = X/20

Work done by 1 man in one day = X/300

A group of 10 men and 5 women can finish the work in 25 days

Work done by 10 men in 25 days = 250X/300

Rest of the work is done by women.

Work done by 5 women = X – 250X/300 = 50X/300 = X/6

Work done by 5 women in one day = X/ (6 × 25) = X/150

Work done by one woman in one day = X/150 × 5 = X/750

Now we need to find the work done by 13 men and 7 women in one day

Work done by 13 men in one day = 13 × (X/300)

Work done by 7 women in one day = 7 × X/750

Total work done by 13 men and 7 women in one day = (65 + 14) X/1500 = 79X/1500

Number of days taken by group to finish the work = 1500/79 = 18.98 = 19 days

Total wages of men and women for one day = 13 × 500 + 7 × 400 = 6500 + 2800 = 9300

∴ Total wages of the group for 19 days = 9300 × 19 = Rs. 176700

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 (10M + 5W) × 25 = (10M + 5M) × 20

⇒ (10M + 5W) × 5 = (15M) × 4

⇒ 50M + 25W = 60M

⇒ 25W = 10M

⇒ 5W = 2M

⇒ M : W = 5 : 2

Total work = (15M × 20)

⇒ (15 × 5 × 20) units

⇒ 1500 units

Number of days taken by 13 Men and 7 women to complete the work = 1500/65 + 14)

⇒ 18.98 = 19 days

Cost of total 13 men and 7 women = Rs. (13 × 500 + 7 × 400) × 19

⇒ Rs. (6500 + 2800) × 19

⇒ Rs. 176,700

∴ Total cost will be Rs. 176,700

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