# Word Problem 64 & 65

**Problem 64: Income of A is 25 % less than B’s income. How much percent B’s income would be more than that of A ?**

**Solution:**

To solve this problem we will suppose income of B

i-e

then because A’s income is 25% less than that of B, we write;

Now we can find how much B is earning extra than A – by subtracting A’s income from B’s income.

i-e

Now we use percentage formula – to find what percent this B’s extra income is of A’s income !

So, here we will put B’s extra earning as nominator and A’s income as denominator;

**So, B is earning approximately 33% more than A**

**Problem 65: If the price of the coal be raised by 10%, by how much percent a man must reduce its consumption so as not to increase his expenditure ?**

**Solution: **

This is the problem involving percentage calculation. Here we assume that intially price of caol and expenditure are same.

i-e Let’s suppose;

Rise in price is 10%, so we will find first 10% of x (price)

or

New price will be the sum of increment and original price

i-e

or simply

If the man keeps on burning same quantity of coal then again his consumption will be equal to the new price

i-e he will stay with

Now suppose to keep his expenditure same (i-e ‘x’) the man now will have to reduce his consumption by y% of ‘new consumption’

i-e

Now If we subtract from ‘new consumption’ this ‘reduction’ then consumptiom will stay equal to original expenditure ‘x’

i-e

New Consumption – Reduction in Consumption = x

cancelling ‘x’ term

**So, the man will have to reduce his consumption by **