X takes 10 days less than the time taken by Y to finish a piece of work. X and Y together can do it in 12 days. In how many days Y alone can finish the work?
Answer & explanation
Correct answer: option 4
X + Y = 12 days,
Let Y = a days
Let X = a -10 days
So, Y in a day = \(\frac{1}{a}\)
and X in a day = \(\frac{1}{a - 10}\),
According to the question,
\(\frac{1}{a}\) + \(\frac{1}{a - 10}\) = \(\frac{1}{12}\)
⇒ \(\frac{2a -10}{a x a - 10a}\) = \(\frac{1}{12}\)
⇒ \( {a }^{ 2} \) - 10a = 24a - 120
⇒ \( {a }^{ 2} \) - 34a + 120 = 0
⇒ (a - 30)(a - 4) = 0
So, a = 30 or a = 4 (Not possible)
Therefore, Y can alone finish the work in 30 days.