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 3 of 4.
Ajay said:
9 years ago
I can't be getting this. Can anyone explain me in short and sweet plz?
(or).
Any short cut method for this type of questions?
(or).
Any short cut method for this type of questions?
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:
1 decade ago
Hi,
How the C. P is calculated?
How the C. P is calculated?
Rahul said:
1 decade 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:
1 decade 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 ?
Vijay said:
1 decade ago
Solve in another method: Amount of 1st kind 'x'and its cost Rs.9/kg and amount of 2nd kind is 27kg and its cost is 7/kg.
c.p of mixture=(9x+(27*7))
s.p of mixture=9.24*(27+x)
Profit=(s.p-c.p)/c.p=10/100
Then we get x value.
c.p of mixture=(9x+(27*7))
s.p of mixture=9.24*(27+x)
Profit=(s.p-c.p)/c.p=10/100
Then we get x value.
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