**RRB JE Ratio & Proportion Questions PDF**

Download Top 20 RRB JE Ratio & Proportion Questions and Answers PDF. RRB JE Maths questions based on asked questions in previous exam papers very important for the Railway JE exam

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**Question 1: **The ratio between two numbers is 3:7. If the sum of squares of two numbers is 3712, then what is the largest number?

a) 64

b) 56

c) 48

d) 34

**Question 2: **The ratio of two numbers is 2:5. If the difference between the squares of the numbers is 1029, then find the sum of the two numbers.

a) 35

b) 56

c) 49

d) 28

**Question 3: **Ratio of ages of daughter and mother 4 years ago was 3:8 and the ratio of their ages 6 yrs from now will be 8:13. What is the ratio of ages of daughter to mother after 10 years from now ?

a) 1:3

b) 1:2

c) 2:3

d) 2:5

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**Question 4: **Ratios of incomes of U and V is 7:9 and both of them get a hike of Rs 300 and the ratio of their incomes become 4:5. What is the income of V before hike?

a) 3600

b) 2700

c) 1800

d) 4500

**Question 5: **Three samples of soda and wine mixture have soda to wine ratio as 1:3,4:3 and 2:3. A new sample consisting of 1 litre each of each sample is prepared. What is the soda to wine ratio in the new sample ?

a) 167:251

b) 171:249

c) 169:253

d) 175:253

**Question 6: **Two boys P and Q have their incomes in the ratio 5:6. P and Q save Rs 250 and Rs 200 per month respectively and if their expenditures are in the ratio of 4:5 then what is the income of P ?

a) 2550

b) 2450

c) 2350

d) 2250

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**Question 7: **Prathap distributes his money to his sons A,B,C and D in the ratio of 5:6:4:3 and B gets 6000 more than D. What is the total money distributed ?

a) 30000

b) 32000

c) 36000

d) 34000

**Question 8: **The sum of the ages of Ravi and his younger brother Chinna is 30. The difference in their ages is 14. What is the ratio of the age of Ravi to the age of Chinna?

a) 11:4

b) 4:11

c) 15:7

d) 7:15

**Question 9: **A college has 420 students. The ratio of boys and girls is 9:5. Some new boys and some new girls joined the college because of which the ratio of boys and girls become 3:2. If the number of new boys who enrolled in the college was 30 then find the number of new girls who joined the college.

a) 45

b) 70

c) 20

d) 50

**Question 10: **What is the fourth proportional of 12,36 and 108 ?

a) 144

b) 162

c) 324

d) 216

**Question 11: **What is the mean proportional of 32 and 128 ?

a) 64

b) 96

c) 72

d) 108

**Question 12: **What is the third proportional of 12 and 36 ?

a) 24

b) 15

c) 72

d) 108

**Question 13: **What is the third proportional of 48 and 64?

a) 81

b) 81.33

c) 84

d) 85.33

**Question 14: **In what ratio should a milk solution of concentration 60% be mixed with a milk solution of concentration 25%, such that the resultant solution has a concentration of 50%?

a) 2 : 1

b) 5 : 3

c) 4 : 1

d) 5 : 2

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**Question 15: **The ratio of the ages of Ram and Shyam are 5:7 respectively. Six years ago the ratio of their ages were 2:3. Find the sum of the present ages of Ram and Shyam.

a) 72 years

b) 60 years

c) 84 years

d) 90 years

**Question 16: **A sum of Rs. 750 is distributed among A,B,C and D in such a manner that A gets as much as B and C together. B gets Rs. 125 more than C and D gets as much as C. What is A’s Share?

a) Rs. 100

b) Rs. 225

c) Rs. 275

d) Rs. 325

**Question 17: **The ages of Khushi and jagriti are in the ratio 5 : 8. After 8 years the the ratio of their ages will be 3 : 4. What is the difference in their ages ?

a) 16 Years

b) 8 Years

c) 6 Years

d) 10 Years

**Question 18: **Find the fourth proportional to 8, 18 and 24.

a) 36

b) 54

c) 72

d) 90

**Question 19: **In a 150-litre solution of milk and water, the ratio of water and milk is 3:2. If the ratio of milk and water is to be 1:5, then what is the amount of water to be added?

a) 120

b) 150

c) 180

d) 210

**Question 20: **If ratio of sum of two numbers to difference of two numbers is $\frac{15}{2}$, then find the ratio of the larger number to the smaller number.

a) 15 : 13

b) 17 : 13

c) 19 : 11

d) 16 : 11

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**Answers & Solutions:**

**1) Answer (B)**

Let the two numbers be 3x and 7x respectively.

Given, $(3x)^2+(7x)^2 = 3712$

⇒ $9x^2+49x^2 = 3712$

⇒ $58x^2 = 3712$

⇒ $x^2 = 64$

⇒ x = 8

Then, Largest number = 7x = 7*8 = 56

**2) Answer (C)**

Let the two numbers be 2x and 5x.

Given, $(5x)^2 – (2x)^2 = 1029

⇒ $25x^2 – 4x^2 = 1029

⇒ $21x^2 = 1029

⇒ x^2 = 49

⇒ x = 7.

Then, the two numbers will be,

2x = 2*7 = 14

5x = 5*7 = 35

Then, Sum of two numbers = 14+35 = 49.

**3) Answer (C)**

Let the present age of daughter be ‘d’ and mother’s be ‘m’

(d-4)/(m-4)=3:8

8d-32=3m-12

8d-3m= 20

(d+6)/(m+6)=8:13

13d+78=8m+48

13d-8m=-30

64d-24m=160

39d-24m=-90

25d=250

d=10

m=20

10 years from now their ages will be d=10+10 and m=20+10

Ratio =20:30

=2:3

**4) Answer (B)**

let the incomes of U and V be 7x and 9x.

Now (7x+300)/(9x+300)=4:5

35x+1500=36x+1200

x=300

Income of V =9*300

=2700

**5) Answer (B)**

By taking the amount of soda in each sample we have 1/4,4/7,2/5

and wine as 3/4,3/7,3/5

Total soda content in new sample is ((1/4)+(4/7)+(2/5))=171/140

Total wine content in new sample is ((3/4)+(3/7)+(3/5))=249/140

Ratio =171:249

**6) Answer (D)**

let their incomes be 5x and 6x

Then their expenditures will be 5x-250 and 6x-200

Therefore (5x-250/6x-200)=4:5

25x-1250=24x-800

x=450

P’s income=450*5

=2250

**7) Answer (C)**

Amount received by A,B,C and D be 5x,6x,4x and 3x respectively

B-D=6000 i.e 6x-3x=6000

x=2000

Total sum is 5x+6x+4x+3x=18x=36000

**8) Answer (A)**

Let x, y are the ages of Ravi and chinna

x+y = 30 —-(1)

x-y = 14 —–(2)

add (1) & (2)

x+y+x-y = 30+14

2x = 44

x = 22 then y = 8

Ratio = x/y = 22/8 = 11/4 = 11:4

So the answer is option A.

**9) Answer (D)**

Let us assume that there are 9x boys and 5x girls. So we have 14x = 420 => x = 30

=> The college has 30*9 = 270 boys and 5*30 = 150 girls

=> Now after 30 new boys join the number of boys will become 300.

The new ratio is 3:2. Hence, the number of girls must be 200.

Thus, 50 new girls must have joined.

**10) Answer (C)**

For fourth proportional we have 12:36::108:x

Therefore 12x=36*108

x=324

**11) Answer (A)**

For mean proportional we have 32:x::x:128

Therefore $x^{2}$=32*128

x=64

**12) Answer (D)**

For 3rd proportional we have 12:36::36:x

Therefore 12x=36*36

x=108

**13) Answer (D)**

The third proportion is given by the following equation, 48 : 64 :: 64 : ?

So, ? = 64 * 64/ 48 = 85.33

**14) Answer (D)**

The given scenario can be represented as follows:

So, the required ratio is 25 : 10 = 5 : 2

**15) Answer (A)**

Let the present ages of Ram and Shyam be 5x and 7x respectively.

Ages of Ram and Shyam 6 years ago = 5x-6 and 7x-6

(5x-6)/(7x-6) = 2/3

3(5x-6) = 2(7x-6)

15x-18 = 14x-12

x = 6

Present ages of Ram and Shyam = 30 years and 42 years.

Sum = 30+42 = 72 years.

**16) Answer (D)**

D = C

B = C + 125

A = B + C

A + B + C + D = 750

Solving these 4 equations, we get C = 100

B = 225

A = 325

D = 100

**17) Answer (C)**

Let their ages be 5x and 8x. After 8 years, their ages are 5x + 8 and 8x + 8. But 5x+8:8x+8 = 3:4

Solving for x, we get x = 2

So, difference of ages = 8x – 5x = 3x = 6 years

**18) Answer (B)**

For a, b, c and d to be proportional, a:b :: c:d must hold true.

=> 8 : 18 :: 24 : x

=> 8x = 24 * 18

=> x = 3 * 18

=> x = 54

**19) Answer (D)**

Water : Milk = 3 : 2 => water = 3x and milk = 2x

=> x = 30

=> water = 90 litres and milk = 60 litres.

For ratio to become 1:5, water quantity must be 5*60 = 300 litres.

=> water to be added = 300 – 90 = 210 litres.

**20) Answer (B)**

Let the two numbers be a and b respectively.

$\frac{a+b}{a-b}$ = $\frac{15}{2}$

2a + 2b = 15a – 15b

=> 13a = 17b

$\frac{a}{b}$ = $\frac{17}{13}$

=> a : b = 17 : 13

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