Question

5. Ashok purchased two qualities of grains at the rate
of 100 per quintal and 160 per quintal. In 50
quintals of the second quality, how much grain of
the first quality should be mixed so that by selling
the resulting mixture at * 195 per quintal, he gains
a profit of 30%?
(a) 10 quintals (b) 14 quintals
(c) 20 quintals (d) None of these​

Answer 1

10 quintal of the grain of  the first quality should be mixed.

Explanation:

By selling the resultant mixture of grain at 195 per quintal he gains a profit of 30%.

So, if the cost price of the mixture is x per quintal then

$x(1 + \frac{30}{100}) = 195$

⇒ x = 150 per quintal.

Now, let us assume that Q quintal of the first quality grain is mixed with 50 quintals of the second quality is mixed.

So, the total price of the mixture = 100 × Q + 160 × 50 = 100Q + 8000.

Hence, the cost rate of the mixture will be $\frac{100Q + 8000}{Q + 50}$ which is equal to 150 per quintal.

So, $\frac{100Q + 8000}{Q + 50} = 150$

⇒ 100Q + 8000 = 150Q + 7500

⇒ 50Q = 500

⇒ Q = 10 quintal. (Answer)