Question

Sonu buys 40kg of wheat at 12.50rs per kg and 30kg of wheat at 14rs per kg. At what rate per kg should he sell the mixture to gain 5% on the whole?

Answer 1

Hint: According to given in the question we have to find the rate per kg should he sell the mixture to gain 5% on the whole when Sonu buys 40kg of wheat at 12.50rs per kg and 30kg of wheat at 14rs per kg. So, first of all we have to find the total cost of weight of 40kg at the rate of 12.50rs.
and after that we have to find the total cost of weight of 30kg at the rate of 14rs per kg. After that we have to add the total cost of wheat of weight 40kg at the rate of 12.50rs and the wheat of weight 30kg at the rate of 14rs.
Now, we have to find the 5% on the total rate obtained to find the rate when per kg should he sell the mixture to gain 5% on the whole.

Complete step-by-step answer:
Step 1: First of all we have to find the cost of wheat of weight of 40kg at the rate of 12.50rs.
Hence,
Rate of wheat of weight 40kg at the rate of 12.50rs $ = 40 \times 12.50rs$
Rate of wheat of weight 40kg at the rate of 12.50rs$ = 500rs$
Step 2: Now, same as the step 1 we have to find the cost of wheat of weight of 30kg at the rate of 14rs.
Hence,
Rate of wheat of weight 30kg at the rate of 14rs $ = 30 \times 14rs$
Rate of wheat of weight 30kg at the rate of 14rs$ = 420rs$
Step 3: Now, we have to find the total cost of wheat of weight 40kg at the rate of 12.50rs per kg and of weight 30kg at the rate of 14rs per kg.
Total cost:
$
= 500 + 420 \\
= 920rs \\
$
Step 4: Now, to get the 5% of profit we have to calculate the 5% of the obtained total cost.
$
= 920 \times \dfrac{5}{{100}} + 920 \\
= 960rs \\
$
Step 5: Now, we have to find the total weight of the given weight to find the rate.
Total weight of the given weight $ \Rightarrow (40 + 30) = 70kg$
So, rate $ = \dfrac{{960}}{{70}}rs$
On solving the expression obtained above,
Rate $ = 13.8rs$

Hence, by finding the total cost of weight of 40kg at the rate of 12.50rs. and after that we have to find the total cost of weight of 30kg at the rate of 14rs per kg. we have obtained the rate per kg should he sell the mixture to gain 5% on the whole = 13.8rs

Note: To find the rate required it is necessary to find the cost of weight of 40kg at the rate of 12.50rs. and after that we have to find the total cost of weight of 30kg at the rate of 14rs per kg.
By calculating the 5% of the total cost of wheat of weight 40kg and 30kg we can obtained
the rate required. While substituting the values we must make sure that all the values are of the same units.