Multiple choice

6 men or 10 boys can complete a piece of work in 15 days. if 7 men and x boys complete the same piece of work in 9 days, then x is equal to

  1. 4

  2. 5

  3. 6

  4. 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

6 men = 10 boys, so 1 man = 5/3 boys. 7 men + x boys = (7 * 5/3) + x = (35/3 + x) boys. Work done by 10 boys in 15 days = 150 boy-days. Work done by (35/3 + x) boys in 9 days = 9 * (35/3 + x) = 105 + 9x. Setting 105 + 9x = 150 gives 9x = 45, so x = 5.

AI explanation

Using the proportion 6 men equals 10 boys, the work can be expressed as 6 men working for 15 days, meaning the total work is 90 man-days. Since 10 boys also take 15 days, the total work is 150 boy-days. For the second scenario, the work of 7 men and x boys for 9 days equals 90 man-days, so (7 men plus x boys) times 9 days equals 90 man-days. This gives 7 men plus x boys as 10 men, meaning x boys equals 3 men; converting 3 men to boys using the ratio 1 man equals 10/6 boys gives x as 5. The value of x is 5.

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