Question

Consider a fraction such that when the numerator is increased by 1 and the denominator is increased by 3 we get 2÷3 if only the denominator is increased by 4 we get 1÷2

Answer 1

Let the numerator and the denominator of the fraction be a,b
ATQ,
a+1/b+3=2/3......1
a/b+4=1/2..........2
From 1,
3a-2b=3......3

From2,
2a-b=4
Multiply 2 on bs
4a-2b=8......4

Subtract 3 from 4
We get
a=5

Put a=5 in 3
We get
b=6
Hence the given fraction is a/b=5/6