Question

The cost price of three varieties of mangoes namely M, N and O is Rs.20/ kg, Rs.40/ kg and Rs.50/ kg. respectively. Find the selling price of one kg of mangoes in which there three varieties of mangoes are mixed in the ratio of 2:3:5 such that there is a net profit of 20%?

Answer 1

Hint: We can solve their type of questions by using the unitary method. For the ease of calculation, we have to assume certain values. For example, in this question we are going to assume the weights of the three varieties of mangoes M, N and O as 2kg, 3 kg and 5 kg respectively.

Complete step by step solution:
Let we have 2 kg of M, 3 kg of N and 5 kg of 0.
If we put it together, we will have 10 kg of mangoes in the same ratio 2:3:5.
Therefore, Now calculating the price of 10 kg of mangoes in the ratio 2:3:5
Cost of 10 kg mangoes $ = \left( {2 \times 20} \right) + \left( {3 \times 40} \right) + \left( {5 \times 50} \right)$
$ = 40 + 120 + 250$
= Rs. 410
Now we can calculate the weight of 1 kg mangoes using the unitary method.
Cost of 10 kg mangoes = Rs 410
Cost of 1 kg mango $ = \dfrac{{410}}{{10}}$ = Rs. 41
This is the actual price of the mangoes. Here we have to make a profit of 20 % we first need to calculate the profit amount
$Therefore, $ profit $ = 41 \times \dfrac{{20}}{{100}}$ = Rs. 8.2
Now if we add the profit to the actual cost we will get the selling price
Selling cost $ = 41 + 8.2 = 49.2$

The rate at which mangoes should sell = Rs. 49.2

Note: These types of questions can be easily solved using the unitary method. We always use the unitary method whenever we have given some feature value and we need to find another value. For example, Let us say the price of 4 units of something is given and asked us to find the price of 6 units. So we’ll use the unitary method. In the unitary method, we first try to get the feature value for one unit. then we multiply the number which we have asked to find.