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 1 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.
Avinash Rai said:
8 months ago
@All. Here's my explanation.
Let x kg of 9 Rs. sugar.
Total cost before gain = (9*x + 27*7),
and after gain = (9*x + 27*7) * 1.1 where (10% gain).
This total cost should be equal to 9.24 * (27+x)
By solving, 9.24 * (27+x) = (9*x + 27*7) * 1.1
x = 63.
Let x kg of 9 Rs. sugar.
Total cost before gain = (9*x + 27*7),
and after gain = (9*x + 27*7) * 1.1 where (10% gain).
This total cost should be equal to 9.24 * (27+x)
By solving, 9.24 * (27+x) = (9*x + 27*7) * 1.1
x = 63.
(3)
Sushant said:
3 years ago
9.24 is sp with 10% profit.
Calculate cp with profit per cent formula;
Then, we get 8.4 cp.
Calculate cp with profit per cent formula;
Then, we get 8.4 cp.
(1)
Mangesh said:
4 years ago
Why use the 100/110? Explain, please.
(10)
Namratha said:
4 years ago
Can somebody please explain how 110/100 came, why should we take it like that and what's that?
(4)
Anushka said:
4 years ago
S.P = 9.24
CP = 9.24 * 100/110 = 8.4.
Let the qty of sugar be x;
9x + (27 * 7)/27 + x = 8.4
x= 63kg => answer.
CP = 9.24 * 100/110 = 8.4.
Let the qty of sugar be x;
9x + (27 * 7)/27 + x = 8.4
x= 63kg => answer.
(6)
Simran Mehta said:
5 years ago
@Jeyari.
By reducing it.
14:6- dividing both by 2 which gives 7:3.
By reducing it.
14:6- dividing both by 2 which gives 7:3.
(1)
Jeyari said:
5 years ago
Could you please explain how ratio reduced to 7:3?
Andy said:
6 years ago
First get the mean or the cost price 9.24*110/110 = 8.4.
Then (27*7)+(9*x)/27+x = 8.4(average formula).
Solving x we get 63.
Then (27*7)+(9*x)/27+x = 8.4(average formula).
Solving x we get 63.
Andy said:
6 years ago
The first step find the cost price 9.24 * 100/110 = 8.4.
Then equation: (7*27)+(9*X) = 8.4.
Solving X = 63.
Then equation: (7*27)+(9*X) = 8.4.
Solving X = 63.
(1)
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