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Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costing Rs. 7.77 per kg. and sells the mixture at Rs. 8.80 per kg. and earns a profit of % on his sale price. In what proportion does he mix them?
Verified Answer
Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costin...
Step-by-step explanation:
Let x kg of the 1st type of tea is mixed with y kg of the 2nd type of tea.
Then the cost price of the mixed tea is
= Rs. (6.92x + 7.77y)/(x + y) per kg
Given that, the selling price of the mixed tea is Rs. 8.80 per kg
So profit = selling price - cost price
= Rs. 8.80 - (6.92x + 7.77y)/(x + y)
= Rs. (8.80x + 8.80y - 6.92x - 7.77y)/(x + y)
= Rs. (1.88x + 1.03y)/(x + y)
By the given condition,
profit = selling price * 17.5%
i.e., (1.88x + 1.03y)/(x + y) = 8.80 * 17.5/100
or, (1.88x + 1.03y)/(x + y) = 1.54
or, 1.88x + 1.03y = 1.54x + 1.54y
or, 1.88x - 1.54x = 1.54y - 1.03y
or, 0.34x = 0.51y
or, x/y = 0.51/0.34
or, x/y = 3/2
i.e., x : y = 3 : 2
∴ the required ratio is 3 : 2
This question is part of UPSC exam. View all CA Foundation courses
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Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costin...
Solution:
Given,
Cost of 1 kg tea of type A = Rs. 6.92
Cost of 1 kg tea of type B = Rs. 7.77
Selling price of the mixture = Rs. 8.80
Profit earned = %
To find: The proportion in which types A and B of tea are mixed.
Let us assume that the dealer mixes A kg of tea of type A and B kg of tea of type B.
The cost price (CP) of the mixture will be:
CP = (A × 6.92) + (B × 7.77)
The selling price (SP) of the mixture will be:
SP = (A + B) × 8.80
Profit = SP - CP
Profit % = (Profit/CP) × 100
Substituting the values of CP, SP and Profit in the above equation, we get:
Profit % = [(A + B) × 8.80 - (A × 6.92) - (B × 7.77)]/(A × 6.92 + B × 7.77) × 100
Simplifying the above equation, we get:
Profit % = [(8.80 - 6.92 - )/7.34] × 100
Profit % = (1.88/7.34) × 100
Profit % = 25.60%
Therefore, the dealer earns a profit of 25.60% on his sale price.
To find the proportion in which types A and B of tea are mixed, we can use the method of alligation.
Let x be the proportion in which type A tea is mixed and (1-x) be the proportion in which type B tea is mixed.
By the alligation rule, we have:
(6.92) (8.80)
|------------------|
(1-x) x
(7.77) (8.80)
|------------------|
(1-x) x
Solving the above equations, we get:
x = 0.44
(1-x) = 0.56
Therefore, the dealer should mix type A tea and type B tea in the proportion of 0.44:0.56 to earn a profit of 25.60% on his sale price.
Given,
Cost of 1 kg tea of type A = Rs. 6.92
Cost of 1 kg tea of type B = Rs. 7.77
Selling price of the mixture = Rs. 8.80
Profit earned = %
To find: The proportion in which types A and B of tea are mixed.
Let us assume that the dealer mixes A kg of tea of type A and B kg of tea of type B.
The cost price (CP) of the mixture will be:
CP = (A × 6.92) + (B × 7.77)
The selling price (SP) of the mixture will be:
SP = (A + B) × 8.80
Profit = SP - CP
Profit % = (Profit/CP) × 100
Substituting the values of CP, SP and Profit in the above equation, we get:
Profit % = [(A + B) × 8.80 - (A × 6.92) - (B × 7.77)]/(A × 6.92 + B × 7.77) × 100
Simplifying the above equation, we get:
Profit % = [(8.80 - 6.92 - )/7.34] × 100
Profit % = (1.88/7.34) × 100
Profit % = 25.60%
Therefore, the dealer earns a profit of 25.60% on his sale price.
To find the proportion in which types A and B of tea are mixed, we can use the method of alligation.
Let x be the proportion in which type A tea is mixed and (1-x) be the proportion in which type B tea is mixed.
By the alligation rule, we have:
(6.92) (8.80)
|------------------|
(1-x) x
(7.77) (8.80)
|------------------|
(1-x) x
Solving the above equations, we get:
x = 0.44
(1-x) = 0.56
Therefore, the dealer should mix type A tea and type B tea in the proportion of 0.44:0.56 to earn a profit of 25.60% on his sale price.
Community Answer
Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costin...
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Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costing Rs. 7.77 per kg. and sells the mixture at Rs. 8.80 per kg. and earns a profit of % on his sale price. In what proportion does he mix them?
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Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costing Rs. 7.77 per kg. and sells the mixture at Rs. 8.80 per kg. and earns a profit of % on his sale price. In what proportion does he mix them? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costing Rs. 7.77 per kg. and sells the mixture at Rs. 8.80 per kg. and earns a profit of % on his sale price. In what proportion does he mix them? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costing Rs. 7.77 per kg. and sells the mixture at Rs. 8.80 per kg. and earns a profit of % on his sale price. In what proportion does he mix them?.
Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costing Rs. 7.77 per kg. and sells the mixture at Rs. 8.80 per kg. and earns a profit of % on his sale price. In what proportion does he mix them? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costing Rs. 7.77 per kg. and sells the mixture at Rs. 8.80 per kg. and earns a profit of % on his sale price. In what proportion does he mix them? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Example 2: A dealer mixes tea costing Rs. 6.92 per kg. with tea costing Rs. 7.77 per kg. and sells the mixture at Rs. 8.80 per kg. and earns a profit of % on his sale price. In what proportion does he mix them?.
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