Question

Two oils A and B are mixed in the ratio 3: 2. The cost price of oil A and B are Rs. 300 per litre and Rs.400 per litre respectively. If one-fourth of the mixture is sold at Rs. 450 per litre and the remaining of the mixture at Rs. 500 per litre, find the profit per cent on the whole.

Answer 1

Let the common multiple be x.
So, 3x litres of oil A is mixed with 2x litres of oil B.
Total mixture
= 3x + 2x 
= 5x litres
C.P. of oil A 
= Rs.300 per litre
So, C.P. of 3x litres
= Rs.(300 x 3x)
= Rs.900x
C.P. of oil B 
= Rs.400 per litre
So, C.P. of 2x litre
= Rs.(400 x 2x)
= Rs.800x
So, total C.P. of the entire mixture that is , 5x litres 
= Rs1700x
Now, one - forth of the mixture is sold at Rs.450 per litre
that is , ${\displaystyle \frac{1}{4}}$ of (5x) 
= ${\displaystyle \frac{1}{4}\times 5x}$

= ${\displaystyle \frac{5x}{4}}$ litres is sold at Rs.450 per litre

So, S.P. of ${\displaystyle \frac{5x}{4}}$litres

= ${\displaystyle \frac{5x}{4}\times 500}$
 Rs.1875x

So. S.P. of the entire mixture
= Rs.${\displaystyle \frac{1125x}{2}+\text{Rs.}1875x}$

= Rs.${\displaystyle \frac{4875x}{2}}$

Profit = S.P. - C.P.
= Rs.${\displaystyle \frac{4875x}{2}-\text{Rs.}1700x}$

= Rs.${\displaystyle \frac{1475x}{2}}$

Profit%
= ${\displaystyle \frac{\text{Profit}}{\text{C.P.}}\times 100}$

= ${\displaystyle \frac{\frac{1475x}{2}}{1700x}\times 100}$

= ${\displaystyle \frac{1475x}{3400x}\times 100}$

= ${\displaystyle \frac{1475}{2400}\times 100}$
= 43.38% approx
Hence, the profit percent on the whole is 43.38% approximately.