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⁞ Alligation

Aptitude ➤ Alligation ➤ 1
Question 1
Q1.  Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
 

Answer :  Rs. 175.50
Question 2
Q2.  In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
 

Answer :  7 : 3


Let's denote the ratio in which the two varieties of pulses are mixed as x:y, where x is the ratio for the Rs. 15 per kg pulses and y is the ratio for the Rs. 20 per kg pulses.

Given:
- Price of the first variety of pulses = Rs. 15 per kg
- Price of the second variety of pulses = Rs. 20 per kg
- Price of the mixture = Rs. 16.50 per kg

To find the ratio x:y, we can set up the following equation based on the weighted average:

Now, let's solve for x and y :

15x + 20y = 16.50(x + y)
15x + 20y = 16.50x + 16.50y
20y - 16.50y = 16.50x - 15x
3.50y = 1.50x
y/x = 1.50/3.50

So, the ratio x:y in which the two varieties of pulses must be mixed is 3.5:1.5 or simplifying it, 7:3.
⚔ DISCUSS

Question 3
Q3.  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 :  63 kg
Question 4
Q4.  In what ratio must water be mixed with milk to gain 16 2/3% on selling the mixture at cost price?
 

Answer :  1 : 6
Question 5
Q5.  In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10 % ?
 

Answer :  3 : 2
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