Question

The denominator of a rational number is greater than its numerator by 7 . If the numerator is increased by 17 and the denominator is decreased by 6 , the new number becomes 2.Find the original number.

Answer 1

"Given: The denominator of a rational number is greater than its numerator by 7 . If the numerator is increased by 17 and the denominator is decreased by 6 , the new number becomes 2

To find: The original number

Let denominator be x+7

numerator be x

as per problem

x+17/x-6+7=2

x+17/x+1=2

x+17=2x+2

x=15

Therefore the original number is 15/22."

Answer 2

let the no. be x/y
y=x+7 as in question
x+17/y-6=2
cross*ly
2(y-6)=x+17
2y-12=x+17
2 (x+7)-12=x+17------(y=x+7)
2x+14-12=x+17
2x-x=17-2
●x=15
y=x+7
so y=15+7
●y=22
▶▶then the original no. is 15/22--(x/y)