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 3 of 5.
Jeyari said:
5 years ago
Could you please explain how ratio reduced to 7:3?
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.
HARI said:
1 decade ago
Let the the quantity of 9 per kg sugar be X.
CP = (X*9)+(27*7) = 9X+189
SP = 9.24*(X+27)
GAIN%=(PROFIT/CP)*100
ie ((SP-CP)/CP)*100 = 10
SUBSTITUTE THE VALUES IN ABOVE EQN AND SOLVE FOR X
i.e. X = 63.
CP = (X*9)+(27*7) = 9X+189
SP = 9.24*(X+27)
GAIN%=(PROFIT/CP)*100
ie ((SP-CP)/CP)*100 = 10
SUBSTITUTE THE VALUES IN ABOVE EQN AND SOLVE FOR X
i.e. X = 63.
Suhani said:
2 decades ago
Hi,
How the C. P is calculated?
How the C. P is calculated?
Rahul said:
2 decades ago
This is same as last problem. Here goes:
Selling price is 9.24 and profit is 10% so:
Cost price + Profit = Selling Price
Let cost price be equal to x:
x + 0.1x = 9.24
1.1x = 9.24
x = 924/11 which is 8.4
Then you do alligation which is shown in the explanation to bring the ratio of Rs. 9 sugar to Rs. 7 sugar down to 7:3
So Amount of Rs. 9 sugar (lets call it A) is related to amount of Rs. 7 sugar by the following formula:
A/27 = 7/3 (since we found out the ratio they are in)
Now solve for A by cross multiplying:
3A = 27 x 7
A = (27 x 7)/3 [27/3 reduces down to 9) = 9 x 7 = 63kg
Selling price is 9.24 and profit is 10% so:
Cost price + Profit = Selling Price
Let cost price be equal to x:
x + 0.1x = 9.24
1.1x = 9.24
x = 924/11 which is 8.4
Then you do alligation which is shown in the explanation to bring the ratio of Rs. 9 sugar to Rs. 7 sugar down to 7:3
So Amount of Rs. 9 sugar (lets call it A) is related to amount of Rs. 7 sugar by the following formula:
A/27 = 7/3 (since we found out the ratio they are in)
Now solve for A by cross multiplying:
3A = 27 x 7
A = (27 x 7)/3 [27/3 reduces down to 9) = 9 x 7 = 63kg
Amit said:
2 decades ago
its simple
(quantity of cheaper/quantity of dearer=cp of dearer-mean price)/(cp of cheaper/cp of mean).
So 27/x=0.6/1.4
x=63.....
So simple
(quantity of cheaper/quantity of dearer=cp of dearer-mean price)/(cp of cheaper/cp of mean).
So 27/x=0.6/1.4
x=63.....
So simple
Raji said:
1 decade ago
Sorry I cant understood what amit said. Kindly explain it.
Sri said:
1 decade ago
Mean price?
May said:
1 decade ago
Can explain me for ratio ??
Ram said:
1 decade ago
How the 14:6 come can any one explain ?
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers