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

101.

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

Answer: Option 'A'

When there are 8 people, the share of each person is 1/8
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 ,
Which is 1/7 of 1/8 of the original share of each person.

102.

A bag contains 5p,10p and Rs20p coins in the ratio of 1:2:4 respectively. If the total money in the bag is Rs.84/-. Find the number of 10p coins in that bag? 

   A.) 160 coins
   B.) 20 coins
   C.) 128 coins
   D.) None of these

Answer: Option 'A'

5paisa : 10paisa : 20paisa = 1 : 2 : 4  ---> coins ratio  
= 5 : 20 : 80 ---> money ratio 
5 paisa × 80 coins = Rs.4/- 
10 paisa × 160 coins = Rs.16/- 
Then 10 paisa coins in that bag = 160 cions

103.

The number of candidates writing three different entrance exams is in the ratio 4:5:6. There is a proposal to increase these numbers of candidates by 40%, 60%, and 85%, respectively. What will be the ratio of increased numbers? 

   A.) 56:80:11
   B.) 56:90:111
   C.) 56:60:111
   D.) 56:70:111

Answer: Option 'A'

Given ratio of number of candidates is 4:5:6
Let the number of candidates for 3 exams be 4k, 5k, and 6k, respectively.
After increasingthenumberof candidates by 40%, 60% and 85%, respectively.
=> Number of candidates become (140% of 4k),(160% of 5k),(185% of 6k)
=> (140x4k) /100, (160x5k)/100 and (185x6k) /100
= 56k/10, 80k/10, and 111k/10
Now, the required new ratio is: 56k/10: 80k/10 : 111k/10
56 : 80 : 111

104.

A mixture contains milk and water in the ratio 3:2. On adding 10 liters of water, the ratio of milk to water becomes 2:3. Total quantity of milk & water before adding water to it?

   A.) 10
   B.) 50
   C.) 20
   D.) 40

Answer: Option 'C'

milk:water = 3:2 
after adding 10 liters of water
milk:water = 2:3 
Olny water patrs increase when mixture of water
milk:wate = 3:2 = 2*(3:2) = 6:4 
after adding 10 liters of water 
milk:water = 2:3 = 3*(2:3) = 6:9 
milk parts always same 
Short cut method: 
milk:water = 6 : 4  
after adding 10 liters of water 
milk:water = 6 : 9  
milk is same but water increse 10liters then the water ratio is increse 5 parts  
5 part ---> 10 liters  
The quantity of milk in the original mixture is = 6 : 4 = 6 + 4 = 10 
10 parts ---> 20 liters  (Answer is = 20) 
Short cut method - 2 : for Only milk problems 
milk : water 
6 : 4 
6 : 9 
milk ratio same but water ratio 5 parts incress per 10 liters 
5 part of ratio ----> 10 liters 
10 part of ratio ---> 20 liters 

105.

If 0.4:1.4 :: 1:4:x, then x=?

   A.) 49
   B.) 4.9
   C.) 0.49
   D.) 0.4

Answer: Option 'B'

0.4 × x = 1.4 × 1.4 
x = 1.4 × 1.4/0.4 = 14/10 × 14/10 × 1/(4/10) 
14/10 × 14/10 × 10/4 
7/10 × 7 = 49/10 = 4.9

106.

A bag contains one rupee, 50 paise and 25 paise coins in the ratio 5:7:9. If the total amount in the bag is Rs. 430, find the number of coins of 25 paise

   A.) 200
   B.) 300
   C.) 360
   D.) 420

Answer: Option 'C'

360

107.

Radhika purchased one dozen bangles. One day she slipped on the floor fell down. What cannot be the ratio of broken to unbroken bangles? 

   A.) 1 : 2
   B.) 1 : 3
   C.) 2 : 3
   D.) 1 : 5

Answer: Option 'C'

There are totally 12 bangles, sum of the two numbers in the ratio should be a factor of 12,
Only 2:3 does not satisfy the criteria.

108.

For every 2 chocolate Ram gets Shyam is given 3 chocolate. If the total number of chocolate distributed to them is 65, then find the number of chocolates Shyam received.

   A.) 30
   B.) 39
   C.) 34
   D.) 45

Answer: Option 'B'

39

109.

A total amount of Rs. 6900 is to be divided among A,B and C in such a way that one-third of A's part, half of B's part and three-fourth of C's part is equal. Then B's part is:

   A.) Rs. 2178.95
   B.) Rs. 2861.76
   C.) Rs. 2239.14
   D.) Rs. 2356.85

Answer: Option 'A'

Given, A + B + C = 6900 ----> (1)
and(1/3) A = (1/2) B = (3/4) C
=> A = (3/2) B -----> (2)
and C = [4/(2 × 3)] B
=> C = (2/3) B -----> (3)
Substitute (2) and (3) in (1)
=> (3/2)B+ B + (2/3)B = 6900
=> B [(3/2) + 1 + (2/3)] = 6900
On taking L.C.M we get,
=> B [(9 + 6 + 4) / 6] = 6900
=> B [19 / 6] = 6900
=> B = 6900 * (6/19)
=> B = 2178.95
Then B's Part = Rs.2178.95

110.

Two numbers are in the ratio 2:3. If eight is added to both the numbers, the ratio becomes 3:4. The numbers are

   A.) 15 and 20
   B.) 16 and 24
   C.) 13 and 17
   D.) 17 and 9

Answer: Option 'B'

Numbers be m and n, m/n = 2/3 (m+8)/(n+8) = ? => m=16 and n= 24

111.

Two numbers are in the ratio 11:6, if 28 is added to each they are in the ratio 47:32. Find the two numbers.

   A.) 44 and 24
   B.) 66 and 36
   C.) 77 and 42
   D.) 94 and 64

Answer: Option 'B'

Numbers are in the ratio 11 : 6 
Two numbers are 11k and 6k 
Adding 28 to both the numbers, 11k+28 and 6k+28 
Given that 11k+28 : 6k+28 = 47 : 32 => 32(11k+28) = 47(6k+28) => (352-282)k = 28 x (15) => k = 6 
First number , 11 x k = 66 Second Number 6 x k = 36 
Numbers are 66 and 36

112.

Find the mean proportional between 49 & 81? 

   A.) 16
   B.) 10
   C.) 63
   D.) 12

Answer: Option 'C'

Formula = √a×b
A = 49 and B = 81 
√49×81 = 7 × 9 = 63

113.

A mixture contains milk and water in the ratio 3:2. If 4 liters of water is added to the mixture, milk and water in the mixture becomes equal. The quantity of milk in the mixture in liter is? 

   A.) 6
   B.) 12
   C.) 24
   D.) 36

Answer: Option 'B'

Given, Milk and Water ratio = 3 : 2
=> quantity of milk= 3x liters
quantity of water = 2x liters
If 4 liters of water is added to the mixture,
New Milk and Water ratio = 1 : 1 (Since equal),
quantity of milk in the new mixture,= 3x liters
quantity of water in the new mixture = 2x + 4 liters.
=>quantity of Milk in new mixture/ quantity of water in new mixture = 1 / 1
=> 3x / (2x + 4) = 1 / 1
=> 3x = (2x + 4)
=> 3x - 2x = 4
=> x = 4
Thus,quantity of milk= 3x liters = 3 × 4 = 12 liters

114.

Rs.780 is divided among 2 men, 6 women and 8 boys so that the share of a man, a woman and a boy are in the ratio 3: 2: 1. Then, how much does a boy get?

   A.) Rs. 30
   B.) Rs.60
   C.) Rs.40
   D.) Rs.240

Answer: Option 'A'

From given data,
780 = 2m + 6w +8b
And m : w : b = 3 : 2 : 1
=> m = 3x Rs.
w = 2x Rs.,
b = x Rs.
Subs these m, w, b values in 780 = 2m + 6w +8b
=> 780 = 2 (3x) + 6 (2x) + 8 x
=> 780 = 6x + 12x + 8x
=> 780 = 26x
=> x = 780 / 26
=> x = 30 Rs.
Thus, a boy will get Rs. 30


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