How much wheat (in kg, rounded off to the nearest integer) costing ₹36 per kg must be mixed with 55 kg of wheat costing ₹45 per kg so that there may be a gain of 20% by selling the mixture at ₹50 per kg?

Correct option is D

Given:

Wheat 1 cost = ₹36/kg

Wheat 2 cost = ₹45/kg

Quantity of Wheat 2 = 55 kg

Selling Price = ₹50/kg

Gain = 20% 

Formula Used: ​

Cost Price = $$\frac{100}{100 + \text{Gain \%}} \times \text{SP}$$​​

Solution:

Cost Price of mixture = $$\frac{100}{120} \times 50$$​ = ₹41.67

Alligation Ratio = $$\frac{45 - 41.67}{41.67 - 36} = \frac{3.33}{5.67} = \frac{37}{63}$$​​

Required amount of ₹36 wheat = $$\frac{37}{63} \times 55 \approx 32.3 \approx 32 \text{ kg}$$ 

Alternate Solution: ​

CP of mixture = $$\frac{125}3$$(from above)

Allegation;

Now Quantity of wheat 1 = $$\frac{10}{17}\times 55 = 32.35 \approx 32\ kg$$ ​