Ratio, Proportion, Variation Aptitude basics, practice questions, answers and explanations 
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Ratio:

1. Duplicate ratio of a : b is a² : b²

2. Sub-duplicate ratio of a : b is sqrt of(a) : sqrt of (b)

3. Triplicate ratio of a : b is a³: b³

4. Sub-triplicate ratio of a : b is cuberoot of (a) : cuberoot of (b)
 

If a/b = c/d; then a=bc/d

(i) (a+b)/b  = (c+d)/d

(ii) (a-b)/b = (c-d)/d

(iii) a/c = b/d

(iv) b/a = d/c

(v) (a+b)/(a-b) = (c+d)/(c-d)

If a/b=c/d; then simplest possible value of a=c, b=d

(vi) In the ratio a : b, if a > b, then  (a + x / b + x) < a / b (x > 0)

(vii) In the ratio a : b, if a < b, then  (a + x / b + x) > a / b (x > 0)

(viii) In the ratio a : b, if a = b, then  (a + x / b + x) = a / b (x > 0)

Proportion & Variation:

If a is directly proportional to b; then a=kb

If a is inversely proportional to b; then a=k/b

If a is directly proportional to b and inversely proportional to c, then a is directly proportional to b/c

=> a= kb/c

Exercise Questions

1. Ram, Sham and Suresh start business investing in the ratio 1/2 : 1/3: 1/6. The time for which each of them invested their money was in the ratio 8:6:12 respectively. If they get profit of Rs.18000 from the business, then how much share of profit will Ram get?
a. Rs.4000
b. Rs.6000     
c. Rs.8000
d. Rs. 10000

2. The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
a. 8 : 9
b. 17 : 18
c. 21 : 22   
d. Cannot be determined

3. p,q and r are three positive numbers and Q=(p+q+r)/2; If (Q-p):(Q-q):(Q-r) = 2:5:7, then find the ratio of p,q and r ?
a. 4:3:7
b. 12:9:7  
c.9:7:4    
d. 4:3:2

4.A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
a. Rs. 460  
b. Rs. 484  
c. Rs. 550  
d. Rs. 664

5. Two numbers are respectively 20% and 50% more than a third number.The ratio of the two numbers is
a. 2 : 5    
b. 3 : 5    
c. 4 : 5    
d. 6 : 7

6. The ratio of the cost prices of two articles A and B is 4:5.The articles are sold at a profit with their selling prices being in the ratio 5:6.If the profit on article A is half of its cost price, find the ratio of the profits on the articles A and B?
a. 7:10        
b. 9:11        
c. 5: 9
d. 10:11

7. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is the total amount?
a. Rs. 14000  
b. Rs. 15000  
c. Rs. 20000  
d. None of these

8. If Rs. 782 be divided into three parts, proportional to ½:2/3:3/4, then the first part is:
a. Rs. 182  
b. Rs. 190  
c. Rs. 196  
d. Rs. 204

9.A bag contains 50 paisa, 20 paisa and 10 paisa coins in the ratio 5:3:1.If the total amount in the bag is 640 Rs,find the difference in the amounts contributed by 50 paisa and 20 paisa coins.
a. Rs.300  
b. Rs.400  
c. Rs.380  
d. None of these

10. The speed of an engine is proportional to the square root of the number of wagons attached to it. Without any wagons attached to it the speed of the engine is 60km/hr. With 16 wagons attached to it the speed of the engine is 40km/hr; find the maximum number of wagons that can be attached so that the train moves.
a. 144         
b. 145         
c. 142         
d. 143

Answer Key:

1.c; 2.c; 3.b; 4.b; 5.c; 6.d; 7.a; 8.d; 9.c; 10.d