Question

A producer of tea blends two varieties of tea from two tea gardens one costing Rs. 18 per kg and another Rs. 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs. 21 per kg, then his gain percent is
A. 12%
B. 13%
C. 14%
D. 15%

Answer 1

Hint: We will first assume how much variety of both the tea he has bought. Now, multiply them with their respect cost and get the cost price accordingly. Now, we will get the selling price by multiplying the quantity by 21. Now using these CP and SP, we can get the required gain percent using its formula.

Complete step-by-step answer:
Since, we are given that the producer of tea blends two varieties of tea from two tea gardens one costing Rs. 18 per kg and another Rs. 20 per kg in the ratio 5 : 3.
So, let us assume he gets $5x$ kg from garden number one and $3x$ kg from garden number two.
So, he bought a total of $8x$ kg.
Now, let us calculate how much he paid in garden 1 and garden 2 because the cost price is going to be the sum of both the amounts he spent at the gardens.
He bought from garden 1 at the rate of Rs. 18 per kg.
So, for $5x$ kg, he must have paid = Rs. $18 \times 5x = Rs.90x$.
He bought from garden 2 at the rate of Rs. 20 per kg.
So, for $3x$ kg, he must have paid = Rs. $20 \times 3x = Rs.60x$.
Total amount he paid at both the gardens = Rs. $(90x + 60x) = Rs.150x$.
Hence, the cost price will be $Rs.150x$.
He actually bought the total tea of $8x$ kg at the rate of Rs. 21 per kg.
So, the selling price will be:- $Rs.8x \times 21 = Rs.168x$.
We know that Gain = Selling Price – Cost Price.
Therefore, here we have Gain = Rs. $(168x - 150x)$ that is equal to $Rs.18x$.
Now, we will use the formula of Gain% which is given by $Gain\% = \dfrac{{Gain}}{{C.P.}} \times 100$, where C.P. refers to the cost price.
So, we have:- $Gain\% = \dfrac{{18x}}{{150x}} \times 100 = 12\% $.

So, the correct answer is “Option A”.

Note: The students must note that since, in the Gain%., we require the ratio. So, instead of considering the quantities of 5x kg and 3x kg, they may assume them directly to be 5 kg and 3 kg because ‘x’ will eventually get cancelled because of being in both places that are in cost price and the selling price.