Question

A shopkeeper blends two varieties of tea costing Rs 18 and Rs 13 per 100 gms in the ratio 7:3. He sells the blended variety at the rate of Rs 18.15 per 100 gm. His percentage gain in the transaction is:
(a) 8 %
(b) 12 %
(c) 15 %
(d) 10 %

Answer 1

Hint: The prices of the two varieties of the tea is given to us. We will use the unitary method to find the cost of 1 gm of tea of each variety. It is given to us that the shopkeeper blends them in the ratio 7 : 3. Thus, we will find the weight of each variety of tea in 100 gm when they are mixed in the ratio of 7 : 3. Then we will find the total cost price of the tea by finding the cost of each variety in 100 gm of blended tea. To find the gain, we have to find the difference between the cost price and the selling price. Once we have the gain, percentage gain is given by the relation $p=\dfrac{g}{cp}\times 100\%$, p is percentage gain, g is gain and cp is the cost price.

Complete step-by-step answer:
Let the two types of team be m and n. Cost of m type of tea is Rs 18 per 100 gm and n type of tea is Rs 13 per 100 gm.
Therefore, the cost of 1 gm of m type of tea will be given by $\dfrac{18}{100}$ = Rs 0.18.
Similarly, the cost of 1 gm of n type of tea will be given by $\dfrac{13}{100}$ = Rs 0.13.
Now, it is given that they are mixed in the ratio of 7 : 3.
If there is 100 gm of tea, then 7k + 3k = 100, where k is a constant.
$\Rightarrow $ 10k = 100
$\Rightarrow $ k = 10
Therefore, in 100 gm, the quantity of m type of tea is 7(10) = 70 gm and the quantity of n type of tea is 3(10) = 30 gm.
Now, the total cost price will be the sum of 70 gm of m type of tea and 30 gm of n type of tea.
$\Rightarrow $ cp = 70 (0.18) + 30 (0.13)
$\Rightarrow $ cp = 12.6 + 3.9
$\Rightarrow $ cp = 16.5
Therefore, the total cost price is Rs 16.5 and the selling price is Rs 18.15.
Hence, the gain will be given as the difference between the selling price and the cost price.
$\Rightarrow $ g = 18.15 – 16.5
$\Rightarrow $ g = 1.65
Now, the total gain percentage will be given as $p=\dfrac{g}{cp}\times 100\%$, p is percentage gain, g is gain and cp is the cost price.
$\begin{align}
  & \Rightarrow p=\dfrac{g}{cp}\times 100\% \\
 & \Rightarrow p=\dfrac{1.65}{16.5}\times 100\% \\
 & \Rightarrow p=10\% \\
\end{align}$

So, the correct answer is “Option d”.

Note: It is not important to use unitary method to find the cost of 1 gm of tea. Students can directly multiply the cost of 100 gm by the percentage of that type of tea in the blend to find the contribution of that type of tea in the total cost price.