In what ratio must wheat costing rs20,rs30 and rs35 per kg be mixed to form a mixture costing rs 25 per kg?
Answers
Answer:
Solution:
Option(C) is correct
If the selling price of the mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture =301.2 = Rs.25/kg.
We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg.
Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg.
The mean desired price falls between B and C.
Step 1:
Find out the ratio Qa:Qc using alligation rule.
QaQc=30−2525−20=11
Be warned if we do not simplify the ratio and let if remain QaQc=55, it changes the final answer, which will be the CORRECT answer as well. See at the end of this answer for more details.
Step 2:
Find out the ratio Qb:Qc using alligation rule.
QbQc=(30−2525−24)=51
Step 3:
Qc is found by adding the value of Qc in step 1 and step 2 =1+1=2
Many people (Rahul Kumar, Maksud, Dheeraj, Pragya) are arguing over this step as for why Qc is being added, find details for the same at the end of the solution.
Therefore, the required ratio =1:5:2
If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture.
Note:
When appearing in actual exam problems of this kind are to be skipped, at least in the first go.
If you were able to solve a decent number of other problems, then you should look at this problem. Moreover, such tye of questions may have MORE THAN ONE SOLUTION which may not match the given answer choices with the correct alternate answer of yours. For an alternate (and CORRECT) answer check SundararajC's comment.
Edit1: Thank you VINAY and bimal for mentioning the anomaly, changed the option from choice B to choice C
Edit2: As pointed by SundararajC, 1.6666 kg of 2nd variety is ASLO a correct answer (check out how) but since it is not given in the answer choices we have settled with 5 Kgs.
Edit 3: Many people are arguing over the addition of Qc in step 3.
From step 1, we have,
QaQc=11
Say we have, 1kg of both Qa & Qc.
From step 2, we have,
QbQc=51
Say we have, 5 kgs of Qb and 1 kg of Qc.
Now if we mix both these mixtures, we have following quantities in the FINAL mixture.
Qa=1 kg from mixture 1 only
Qb=5 kg from mixture 2 only
Qc=1 kg from mixture 1 AND 1 kg from mixture 2
Thus, Qc=(1+1)=22kgs.
Thus, Final ratio of Qa:Qb:Qc=1:5:2 and NOT 1:5:1 as some people are saying.
Hope this helps.
There is not a unique solution but can be infinite possible combinations.
Few of the possible ratios are 3 : 1 : 1 , 4 : 2 : 1 and 5 : 1 : 2
Given:
- Wheat costing rs20,rs30 and rs35 per kg mixed
- Mixture Cost Rs 25 per kg
To Find:
- Ratio in which wheat is mixed
Step 1:
Assume that wheat costing rs20,rs30 and rs35 per kg mixed in ratio
x : y : z
Step 2:
Find Total cost and total Rice
20x + 30y + 35z Rs
x + y + z kg
Step 3:
Find Total cost at 25 Rs per kg and Equate with total cost
25(x + y + z) Rs
20x + 30y + 35z = 25x + 25y + 25z
=> 5y + 10z = 5x
=> y + 2z = x
Step 4:
As there are 3 variable Hence multiple solutions can be
Taking y = 1 and z = 1
x = 3
Hence 3 : 1 : 1
Taking y = 2 and z = 1
x = 4
Hence 4 : 2 : 1
Taking y = 1 and z = 2
x = 5
Hence 5 : 1 : 2
So There is not a unique solution but can be infinite possible combinations
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