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Three men and 5 women together can finish a job in 3 days. Working on the same job 3 women take 5 days more than the time required by 2 men. What is the ratio of efficiency of a man to a woman?
- A2 : 1
- B3 : 2
- C5 : 2
- D4 : 1
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CCommunity
According to the question,
Three men and 5 women together finished the job in 5 days
Let, required no. of days by 2 men = x
⇒ Efficiency of 1 man = 2x
⇒ Required no. of days by 3 women = x + 5
⇒ Efficiency of 1 woman = 3x + 15
Let the total work be 90 units
⇒ 3M + 5W = 90/3 = 30 units
⇒ Work of 1 man = 90/2x units = 45/x
⇒ Work of 1 woman = 90/(3x + 15) units = 30/(x + 5)
So,
⇒ 3(45/x) + 5[30/(x + 5)] = 30
⇒ 45x + 225 + 50x = 10(x + 5)x
⇒ 2x2 - 9x - 45 = 0
⇒ (2x - 15) (x + 3) = 0
⇒ x = 15/2, -3
Since, -3 cannot be possible
⇒ x = 15/2
⇒ Work of 1 man = 45/7.5
⇒ Work of 12 woman = 30/12.5
⇒ Ratio = 45/7.5 : 30/12.5 = 5 : 2
∴ Ratio of man and woman is 5 : 2
Three men and 5 women together finished the job in 5 days
Let, required no. of days by 2 men = x
⇒ Efficiency of 1 man = 2x
⇒ Required no. of days by 3 women = x + 5
⇒ Efficiency of 1 woman = 3x + 15
Let the total work be 90 units
⇒ 3M + 5W = 90/3 = 30 units
⇒ Work of 1 man = 90/2x units = 45/x
⇒ Work of 1 woman = 90/(3x + 15) units = 30/(x + 5)
So,
⇒ 3(45/x) + 5[30/(x + 5)] = 30
⇒ 45x + 225 + 50x = 10(x + 5)x
⇒ 2x2 - 9x - 45 = 0
⇒ (2x - 15) (x + 3) = 0
⇒ x = 15/2, -3
Since, -3 cannot be possible
⇒ x = 15/2
⇒ Work of 1 man = 45/7.5
⇒ Work of 12 woman = 30/12.5
⇒ Ratio = 45/7.5 : 30/12.5 = 5 : 2
∴ Ratio of man and woman is 5 : 2