Question

if a's income is 20 % less than that of b. by what per cent is b's income more than a's?

Answer 1

Suppose B's income is x.
Now, A's income is 20 % less than that of B's.
So, A's income = x−x×20100 = x−x5 = 4x5
Then, difference between A's income and B's income = x−4x5 = x5
So, B's income is x5 more than A's income.
Therefore required percentage = x5×1004x5 = x5×54x×100 = 25%
Therefore B's income is 25% more than A's income.

Second method:
Suppose B's income is 100.
Now, A's income is 20 % less than that of B's.
So, A's income = 100−100×20100 = 100−20= 80
Then, difference between A's income and B's income = 100−80 = 20
So, B's income is 20 more than A's income.
Therefore required percentage = 20×10080 = 25%
Therefore B's income is 25% more than A's income.

Answer 2

Let the b's income be x

so a's income will be x - 20x/100

= x - x/5

= 4x/5

b's income is greater than a's x - 4x/5 = x/5

percentage = x/5 / 4x/5 × 100

= x/5 × 5/4x × 100

= 1/4 × 100

= 25

so b's income is more than a's income by 25%