Manish takes 9 days more than his father to do a certain piece of work together they can do the work in 6 days •how many days will Manish take to do that work alone
Answers
Manish will alone take 18 days to do the piece of work.
Step-by-step explanation:
Let the Manish alone do a piece of work in “x” days and the time taken by his father alone to do the same piece of work be “y ” days.
So,
Work done by Manish in 1 day = 1/x
Work done by his father in 1 day = 1/y
It is given that Manish takes 9 days more than his father to do a piece of work, so, we have
x = y + 9 ….. (i)
Also given that they together can do the same piece of work in 6 days, so, we can write the eq. as,
1/x + 1/y = 1/6
⇒ (y+x)/xy = 1/6
⇒ xy = 6(x+y)
⇒ xy = 6x + 6y
Substituting the value of x from (i)
⇒ (y+9)y = 6(y+9) + 6y
⇒ y² + 9y = 6y + 54 + 6y
⇒ y² + 9y – 12y – 54 = 0
⇒ y² – 3y – 54 = 0
Using formula, y = [-b ± √{b² – 4ac}] / [2a] and Here a = 1, b=-3 & c = -54
⇒ y = [3 ± √{(-3)² – (4*1*-54}] / [2*1]
⇒ y = [3 +- √{9 + 216}] / [2]
⇒ y = [3 +- 15}] / [2]
⇒ y = 9 or -6
Neglecting the negative value
⇒ y = 9 days ← time taken by his father to complete the piece of work alone
∴ x = y + 9 = 9 + 9 = 18 days
Thus, Manish alone takes 18 days to do that piece of work.
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