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:
40 comments Page 2 of 4.
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.
Daniel said:
1 decade ago
I have an easy and understandable way I hope for you guys,
Let x be the quantity we are looking for, and qty A be 7/kg while qty B is 9/kg.
Based on unit equivalency;
[(qty A*price of A)+(qty B*price of B)]profit = total amount*9.24.
Thus, (27*7 + x*9)*1.1 = (27 + x)*9.24.
Solve for x, and you will get x = 63.
Let x be the quantity we are looking for, and qty A be 7/kg while qty B is 9/kg.
Based on unit equivalency;
[(qty A*price of A)+(qty B*price of B)]profit = total amount*9.24.
Thus, (27*7 + x*9)*1.1 = (27 + x)*9.24.
Solve for x, and you will get x = 63.
Vikatakavee said:
1 decade ago
Unit C.P : Qty : Total Amount
Item 1. : 9 : x : 9x
Item 2. : 7 : 27 : 189
Mixture : 8.4 : x+27 : 8.4(x+27)
---> 9x+189 = 8.4x + 226.8.
---> 0.6 x = 37.8.
---> x = 63.
Item 1. : 9 : x : 9x
Item 2. : 7 : 27 : 189
Mixture : 8.4 : x+27 : 8.4(x+27)
---> 9x+189 = 8.4x + 226.8.
---> 0.6 x = 37.8.
---> x = 63.
(1)
Pushpa said:
1 decade ago
According to rule of allegation the C.P of cheaper qty is kept on the left side and dearer one on the right side but I could see it in other in the solution provided please explain.
Hari Shankar Yadav said:
1 decade ago
I am very satisfied with these answers.
Kjkj tikhir said:
10 years ago
Seriously, this type of question must be for 20 marks question.
Very lengthy answers. But very much appreciated to @Vikatakavee even I didn't cope it.
Very lengthy answers. But very much appreciated to @Vikatakavee even I didn't cope it.
Mehedy said:
10 years ago
Just look,
One value is x & another is 27.
So, we can write like: 1.1 (9x+27*7) = 9.24 (x+27).
Now solve the equation.
One value is x & another is 27.
So, we can write like: 1.1 (9x+27*7) = 9.24 (x+27).
Now solve the equation.
RITIK RANJAN said:
10 years ago
From where does this value 1.40 & 0.60 came from?
And there after ratio?
Please help me out.
Anyone having much better and simpler ideas than this one can openly suggest and guide.
Thank you. Hoping for an early reply.
And there after ratio?
Please help me out.
Anyone having much better and simpler ideas than this one can openly suggest and guide.
Thank you. Hoping for an early reply.
MAZHAURL said:
10 years ago
Since, at the profit of 10%,
Selling price tk 110 than cost price tk 100.
Selling price tk 1 than cost price tk 100/110.
Selling price tk 9. 24 than cost price tk 100*9.24/110 = 8.40.
Let, sugar will be mixed x kg.
X kg sugar at tk 9 than cost price will be tk 9x.
27 kg sugar at tk 7 than cost price will be tk 27*7 = 189.
Total cost price = (9x+189).
According to the question,
(9x + 189)/(x+27) = 8.40.
=> 9x + 189 = 8.40x+ 226.8.
=>. 60x = 37.80.
=> x = 63 kg.
Selling price tk 110 than cost price tk 100.
Selling price tk 1 than cost price tk 100/110.
Selling price tk 9. 24 than cost price tk 100*9.24/110 = 8.40.
Let, sugar will be mixed x kg.
X kg sugar at tk 9 than cost price will be tk 9x.
27 kg sugar at tk 7 than cost price will be tk 27*7 = 189.
Total cost price = (9x+189).
According to the question,
(9x + 189)/(x+27) = 8.40.
=> 9x + 189 = 8.40x+ 226.8.
=>. 60x = 37.80.
=> x = 63 kg.
(1)
Darpana said:
10 years ago
How is the ratio of 9:7 dropped down to 7:3? Could someone please explain?
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers