M can complete a work in 14 days less than the time taken by L. If both M and L together can complete the same work in 24 days, then in how many days M alone can complete the same work?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 56 days.
| Understanding/Application |
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Let the number of days taken by L to complete the work be L days. 1 day work of L = 1/L Number of days taken by M to complete the work = L - 14 ATQ - (1/L) + 1/(L - 14) = 1/24 (2L - 14)/(L2 - 14L) = 1/24 L2 - 62L + 336 = 0 L2 - 6L - 56L + 336 = 0 L(L - 6) -56(L - 6) = 0 (L - 56) (L - 6) = 0 L = 56 or 6 |
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M can do work in 14 days less than L so L cannot be 6. L can do the work in 56 days. |