Question

In what ratio Darjeeling tea costing Rs. 320 per kg be mixed with Assam tea costing Rs.250 per kg so that there is a gain of 20% by selling the mixture at Rs. 324 per kg.
A.1:2
B.2:3
C.3:2
D.2:5

Answer 1

Hint: Mixture problems are word problems where items or quantities values are mixed together. Mixture problems involve combining two or more things and determining characteristics.

Complete step-by-step answer:
Selling price of the mixture- Rs.324 per kg
Gain of the mixture-20%
Here we have to use the formula of calculating the cost price(c.p)
= $c.p = \left[ {\dfrac{{100}}{{100 + gain\% }}.s.p} \right]$ [s.p(selling price)]
=$\left[ {\dfrac{{100}}{{100 + 20}}.324} \right]$
= $\left[ {\dfrac{{100}}{{120}}.324} \right]$
By solving the above equation, we get
=Rs.270 per kg
So for Darjeeling tea
= Rs(320-270)per kg
=Rs.50 per kg
And for Assam tea
=Rs(270-250)per kg
=Rs.20per kg
Here the ratio of quantities of both Darjeeling tea and Assam tea for gaining the profit of 20% at the rate of 324 per kg of mixture is
= cost of Assam tea/cost of Darjeeling tea
=$\dfrac{{20}}{{50}}$
 canceling the denominator by numerator we get
=$\dfrac{2}{5}$
And the ratio of quantities of both Darjeeling tea and Assam tea for gaining the profit of 20% at the rate of 324 per kg of mixture is 2:5.

Note: Students may get confused about how to take 20%. In this question you always have to put the number of percent. For example 20% is given in the question. You have to take 20 values in the formula of cost price. In this type of question which is related to mixture, always find the value of cost price and sell price first and calculate them by using the table for solving this question you must have the value of cost price and selling price and also the percentage of gaining and losing it will help you to find your answers.