15 kg of ₹10 per kg wheat is mixed with 5 kg of another type of wheat to get a mixture costing ₹30 per kg. Find the price (per kg) of the costlier wheat.

Question

Accepted Answer

Let the price per kg of the costlier wheat be x.

Total cost of 15 kg wheat at ₹10/kg = 15 × 10 = ₹150
Total cost of 5 kg wheat at ₹x/kg = 5 × x = 5x

Total weight of mixture = 15 + 5 = 20 kg
Total cost of mixture = 20 × 30 = ₹600

According to the problem:
150 + 5x = 600
5x = 600 - 150 = 450
x = 450 / 5 = 90

However, the answer given is ₹70, so let's re-check the calculation using the alligation method:

Using alligation:
Cheaper price = ₹10
Mean price = ₹30
Costlier price = x

Difference between costlier and mean = x - 30
Difference between mean and cheaper = 30 - 10 = 20

Ratio of quantities = (x - 30) : 20 = quantity of cheaper : quantity of costlier = 5 : 15 = 1 : 3

So,
(x - 30) / 20 = 1 / 3
Cross multiply:
3(x - 30) = 20
3x - 90 = 20
3x = 110
x = 110 / 3 ≈ 36.67

This contradicts the previous result and the options.

Re-examining the problem:
Given 15 kg at ₹10/kg and 5 kg at unknown price x, mixture price ₹30/kg.

Total cost = 15*10 + 5*x = 150 + 5x
Total weight = 20 kg
Average price = 30

So,
(150 + 5x) / 20 = 30
150 + 5x = 600
5x = 450
x = 90

Therefore, the price of the costlier wheat is ₹90 per kg.

Hence, the correct answer is ₹90.

Answer

Answer

Answer