Multiple choice

4 boys and 2 girls together can complete a piece of work in 16 days, while 5 girls and 4 boys together can do it in 10 days. If a boy gets paid Rs. 800 per day, then how much should a girl get paid per day?

  1. Rs. 1333.33

  2. Rs. 1728.50

  3. Rs. 1500.68

  4. Rs. 1066.66

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let B and G be daily wages. 16(4B + 2G) = 10(4B + 5G). 64B + 32G = 40B + 50G. 24B = 18G. G = (24/18)B = (4/3)B. If B = 800, G = (4/3) * 800 = 1066.66.

AI explanation

Let b be the daily work units of a boy and g be the daily work units of a girl. The problem gives the equations 4b + 2g = 1/16 and 4b + 5g = 1/10. Subtracting the first equation from the second gives 3g = 1/10 - 1/16 = 3/80, which means g = 1/80. Substituting this back yields 4b + 2(1/80) = 1/16, so 4b = 3/80 and b = 3/320. Since wages are distributed in proportion to work done, the ratio of a girl's wage to a boy's wage is (1/80) / (3/320) = 4/3. With a boy earning Rs. 800 daily, a girl should be paid 800 * (4/3) = Rs. 1066.66.

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