Study Notes for CAT 2021: Mixtures And Alligations - III

1.Joey purchased two cars for total of Rs. 80 lakhs. Later on, he sold first car at the rate of 16% profit and second car at 32% profit, thereby he gained 20%. What is the selling price of first car?

Answer ||| C

Solution |||

The ratio of cost price of the two cars ,

CP of first car = 

SP of first car = 

2.The ratio of expenditure and savings is 3: 2. If the income increases by 15% and the savings increases by 6%, then by how much percent should his expenditure increases?

Answer ||| B

Solution ||| Exp                       Savings

3.A drum contains 80 liters of ethanol. 20 liters of this liquid is removed and replaced with water. 20 liters of this mixture is again removed and replaced with water. How much water (in liters) is present in this drum now?

Answer ||| C

Solution ||| Total volume of mixture=80 
Liquid removed is 20 liter and this process is repeated two times 

So pure ethanol in mixture after two process=  
So water in the final solution=80-45=35

4.In what ratio should coffee powder costing Rs 2500/kg be mixed with coffee powder costing Rs 1500/kg so that the cost of the mixture is Rs 2250/kg?

Answer ||| C

Solution ||| From mixture & allegation 

 

5.Three containers P, Q and R which contain spirit, water and alcohol respectively. the quantity of each is 140 ltr. If 10% spirit is taken out and poured into container Q. Then, again 10% from Q is transferred to R, from which again 10% is transferred to P. What is the proportion of water in container P at the end of the process?

A.  

B.  

C.  

Answer ||| C

Solution ||| Spirit Reamining after 10% of content of P taken out = 126 ltr 
Now spirit and water in Q = 140 ltr water and 14 ltr spirit 
10% of Content of Q = 14 Ltr water and 1.4 ltr spirit 
After 10% of content Q poured into content R,then the content of R = 140 alcohol,14 ltr water,1.4 ltr spirit 
10% of content R includes 14 ltr alcohol,1.4 ltr water, 0.14 spirit 
Now after pouring 10% of content of R into P, the content of P = (126+0.14) ltr spirit, 14 ltr alcohol and 1.4 ltr water 
Proportion of water in container P =  =  =

6.A mixture contain wine and water in the ratio of 7:3 & another mixture contaits ratio of 3:5 How many lit of the first to be mixed with 50 litr of second to make the mixture in equal qty of wine and water?

Answer ||| B

Solution |||  
10 : 16 
5 : 8 
Qty of M₁=50/8=6.25*5=31.25

7.The average of marks scored by the students of a class is 68. The average of marks of the girls in the class is 80 and that of boys is 60. What is the percentage of boys in the class?

Answer ||| B

Solution ||| Let the number of boys and girls in the class be x and y, respectively. 
 
∴ Required percentage  
 
Short Cut 
According to the question, 

 

Ratio of girls and boys 
∴ Percentage of boys

8.A dishonest milkman professes to sell his milk at cost price but he mixes it with water and there by gains 25%. The percentage of water in the mixture is how much?

Answer ||| B

Solution ||| Let CP of 1 L milk be Rs. 1. 
Then, 
SP of 1 L mixture = Rs. 1 gain = 25% 
CP of 1 mixture = Rs.= Rs.  
CP of 1 L pure milk 
CP of 1 L of water 
 
∴ Milk : Water  
Hence, percentage of water in the mixture 

9.A butler stole wine from shop containing 50% of spirit, then he replenished it by different wine containing 20% spirit. Thus there was only 30% strength (spirit) in the new mixture. How much of the original wine did he steal ?

Answer ||| B

Solution |||  By allegation method

Since the ratio of 20% wine to 50% wine is 2 : 1, it means there is  wine is replaced with wine in which the strength of spirit is 20%

So we can say he stole rd of the original wine.

10.The price of petrol is Rs. 60 per litre and the price of oil is Rs. 40 per litres. In what ratio the petrol and oil be mixed such that the profit after selling the mixture at Rs. 75 per litre be 25%

Answer ||| D

Solution |||  Profit% = 25%

Selling price = Rs. 75

Cost price = 75 × 

Now we known that if we mix oil (worth Rs. 40 per litres) with petrol (worth Rs. 60 per litres), the cost price of the mixture must be less than Rs. 60 per litres, which is impossible