Question

for doing some work ganesh takes 10 days more than gajanan. if both work together they complete the work in 12 days. find the number of days taken by ganesh to complete the work alone.​

Answer 1

Answer:

30 days

Step-by-step explanation:

Your question is :-

For doing some work ganesh takes 10 days more than gajanan. if both work together they complete the work in 12 days. find the number of days taken by ganesh to complete the work alone ?

let no. of days taken by ganesh to complete the work = x days

no. of days taken by gajanan to complete the work = x - 10 days

no. of taken by both to complete the work together = 12 days

$\frac{1}{x} + \frac{1}{(x - 10)} = \frac{1}{12} \\ \\ \frac{x - 10 + x }{x(x - 10)} = \frac{1}{12} \\ \\ \frac{2x - 10}{ {x}^{2} - 10x } = \frac{1}{12} \\ \\ 12(2x - 10) = {x}^{2} - 10x \\ \\ 24x - 120 = {x}^{2} - 10x \\ \\ {x}^{2} - 34x + 120 = 0 \\ \\ {x}^{2} - 30x - 4x + 120 = 0 \\ \\ x(x - 30) - 4(x - 30) = 0 \\ \\ (x - 4)(x - 30) = 0 \\ \\ x = 4 \: \: or \: \: x = 30$

No. of days taken by ganesh to complete the work = 4 days or 30 days

No. of days taken by gajanan to complete the work = x - 10

= 4 - 10 or 30 - 10

= -6 or 20 days

since days can't be in negetive so we only consider 30 days as answer

Answer = 30 days