Aptitude - Alligation or Mixture - Discussion
Discussion Forum : Alligation or Mixture - General Questions (Q.No. 7)
7.
How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?
Answer: Option
Explanation:
S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.
 C.P. of 1 kg of mixture = Rs. |
 |
100 | x 9.24 |  |
= Rs. 8.40 |
| 110 |
By the rule of allilation, we have:
| C.P. of 1 kg sugar of 1st kind Cost of 1 kg sugar of 2nd kind | ||
| Rs. 9 | Mean Price Rs. 8.40 | Rs. 7 |
| 1.40 | 0.60 | |
Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27
 x = |
|
7 x 27 | |
= 63 kg. |
| 3 |
Discussion:
41 comments Page 5 of 5.
Sylvester said:
2 months ago
The correct answer is 63 kilograms.
Working Method.
Let the quantity = x
Using price × quantity = amount
(Rs. 9 ● x) + (Rs. 7 ● 27) = 1.1(x + 7)
Step 1:
1.1(x + 7) = 9.24
(x + 7) = 9.24 ÷ 1.1
(x + 7) = 8.4
x + 7 = 8.4
x = 8.4 - 7
x = 1.4
Checking: 1.1 × Rs. 8.4 = Rs. 9.24
Step 2:
9x + 7 ● 27 = 8.4(x + 27)
9x + 189 = 8.4x + 226.80.
9x - 8.4x = 226.8 - 189.
0.6x = 37.80.
x = 37.80 ÷ 0.6
x = 378 ÷ 6.
x = 63
63 kg of sugar costing 9 rupees per kilogram must be mixed with 27 kg of sugar costing 7 rupees per kilogram to gain 10 per cent by selling the final mixture at 9.24 rupees per kilogram.
Working Method.
Let the quantity = x
Using price × quantity = amount
(Rs. 9 ● x) + (Rs. 7 ● 27) = 1.1(x + 7)
Step 1:
1.1(x + 7) = 9.24
(x + 7) = 9.24 ÷ 1.1
(x + 7) = 8.4
x + 7 = 8.4
x = 8.4 - 7
x = 1.4
Checking: 1.1 × Rs. 8.4 = Rs. 9.24
Step 2:
9x + 7 ● 27 = 8.4(x + 27)
9x + 189 = 8.4x + 226.80.
9x - 8.4x = 226.8 - 189.
0.6x = 37.80.
x = 37.80 ÷ 0.6
x = 378 ÷ 6.
x = 63
63 kg of sugar costing 9 rupees per kilogram must be mixed with 27 kg of sugar costing 7 rupees per kilogram to gain 10 per cent by selling the final mixture at 9.24 rupees per kilogram.
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