# Mixture and Alligations Questions-Part 01

(01) If 5 kg of salt costing Rs. 5/kg and 3 kg of salt costing Rs. 4/kg are mixed, find the average cost of the mixture per kilogram.

Given:
Price of 5 kg of salt = Rs. 5/kg
i.e. n1 = 5 and d = 5

And
price of 3 kg of salt = Rs. 4/kg
i.e. n2 = 3 and c = 4

To find:
average cost of the mixture i.e. m

Formula For Alligation
n1/n2 = (d – m) : (m – c)

=> 5/ 3 = (4 – m)/ (m – 5)
=> 5 (m – 5) = (4 – m) 3
=> 5m – 25 = 12 – 3m
=> 5m + 3m = 12 + 25
=> 8m = 37
=> m = 37/8 = 4.625

The average cost of the mixture is Rs.4.625 per kg.

(2) Two types of oils having the rates of Rs.4/kg and Rs. 5/kg respectively are mixed in order to produce a mixture having the rate of Rs.4.60/kg. What should be the amount of second type of oil if the amount of the first type of oil in the mixture is 40 kg?

Given
Rate of mixed oil = 4.60/kg = m
Rate of first oil to be mixed = c = Rs. 4/kg
Rate of second oil to be mixed = d = Rs. 5/kg

Amount of first oil in the mixture = 40 kg = n1

To find: Amount of second oil in the mixture = n2

Representing the question

Formula For Alligation
n1/n2 = (d – m) : (m – c)

Using the above values we get:
n1: n2 = 4 : 6
n1: n2= 2 : 3

Hence n1=2k
and n2=3k

Here, amount of first oil is 40 kg in the ratio 2k as we found out

2k = 40

k = 40/2 = 20

Therefore, Amount of second oil in the ratio 3k = 3 x 20 = 60kg (putting the value of k)

Ans. Amount of second type of oil is 60 kg.

(3) A man purchased cow and a calf for Rs. 1300. He sold the calf at a profit of 20 % and the cow at a profit of 25 %. In this way, his total profit was (300/13) %. Find the cost price of the cow?

Given:
CP of both cow and calf = Rs. 1300
Cow sold at profit of 25%
Calf sold at profit of 20%

Total profit= 300/13%

Formula For Alligation
CP of Calf/ CP of Cow = (d – m) : (m – c)

CP of Calf/CP of cow = (25/13) / (40/13) = 25/40 = 5/8 —–eq(1)

Since, we have to find CP of cow

By applying componendo and dividendo rule in eq(1)
i.e. if a/b = c/d then (a+b)/b = (c+d)/d

Therefore, (CP of calf + CP of cow)/CP of cow = (5+8)/ 8

1300/ CP of cow = 13/8

100 x 8 = CP of cow

CP of cow = 800 rs

Ans. CP of cow is Rs. 800.

(4) The average salary per head of all employees of a company is Rs. 600. The average salary of 120 officers is Rs. 4000. If the average salary per head of the rest of the employees is Rs. 560, find the total number of workers in the company?

Given:
Average salary of 120 officers = Rs. 4000
Average salary of rest of employees = Rs. 560

No. of rest employees/ No. of officers = 3400/ 40

No. of officers = 120

Now, No. of rest employees/ 120 = 3400/ 40
No. of rest employees = (3400 x 120)/ 40
No. of rest employees = 10200

Therefore, Total no. Of employees = No. of officers + No. of rest of employees

= 120 + 10200

= 10320

Ans. Therefore, the total no. Of employees is 10320.

(5) How many kilograms of sugar worth Rs. 3.60/ kg should be mixed with 8 kg of sugar worth Rs. 4.20 per kg, such that by selling the mixture at Rs. 4.40 per kg, there may be a gain of 10%?

Given:
Cheap Sugar Price (c) = Rs. 3.6/ kg
Dearer Sugar Price (d) = Rs. 4.2/kg
Total Quantity of Dearer Sugar= 8 Kg

Selling Price (SP) of Mixture (m) = Rs. 4.40 per kg

Gain = r = 10 %

Cheaper Quantity/ Dearer Quantity => n1/n2 = 0.2/0.4 =1/ 2

Cheaper Quantity/ 8 = 1/ 2

Cheaper Quantity = 8/ 2 = 4 kg

Thus 4 kg of sugar is to be mixed