RRB NTPC - Ratios and Proportions (114 Questions with Explanation)

1.

The ratio of first and second class train fares between two stations is 40:1 and that of the number of passengers travelling between these stations by first and second class is 1:20. If on a particular day Rs.2700/- be collected from the passengers travelling between these stations, then the amount collected from first class passengers is:? 

   A.) Rs.1800/-
   B.) Rs.600/-
   C.) Rs.900/-
   D.) Rs.600/-

Answer: Option 'A'

First class:Second class = 40:1 
mens ratio = 1:20 
Tickets ratio = 40 : 1 
Mens ratio = = 1 : 20 
Money ratio = = 40 : 20 ==> 2 : 1 
3 parts -----> Rs.2700/- 
1 part -------> Rs.900/- 
2 parts ------> Rs.1800/- 

2.

Salaries of Robert and Sam are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sam's present salary?

   A.) 36000
   B.) 38000
   C.) 34000
   D.) 39000

Answer: Option 'B'

Let the original salary of Robert and Sam be 2k and 3k respectively.
Then (2k+4000) / (3k+4000)=40/57
=> 57(2k+4000) = 40(3k+4000)
=> 114k + 2,28,000 = 120k + 1,60,000
=> 2,28,000 - 1,60,000 = 120k - 114k
=> 68000 = 6k
=> 3k = 34000
Sam's present salary = 3k+4000 = 34000 + 4000 = 38000

3.

Find the third proportional to 9 and 12? 

   A.) 9
   B.) 108
   C.) 16
   D.) 9

Answer: Option 'C'

Formula = Third proportional = (b × b)/a 
A = 9 and B = 12 
(12 × 12)/ 9 = 144/9 = 16

4.

The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is? 

   A.) 8
   B.) 12
   C.) 14
   D.) 16

Answer: Option 'D'

3:4 
Total parts = 7 
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ----> 4 (1 × 4 = 4) 
= The greater of the two number is = 4 
= 4 parts ----> 16 (4 × 4 = 16)

5.

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by 

   A.) One-ninth
   B.) One-seventh
   C.) One-eighth
   D.) Seven-eighths

Answer: Option 'B'

When there are 8 people, the share of each person is 1/8 => (Original Share)
When there are 7 people, the share of each person is 1/7
Increase in the share of each person is 1/7 – 1/8 = 1 / 56
1 / 56 ==> Which is 1/7 of 1/8 ==> 1/7 of the original share of each person.

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