260+ Most Asked Ratio And Proportion Questions [100% Free ]

Navigating the landscape of mathematics, one often comes across the fundamental concepts of “ratio and proportion questions“. Grasping the understanding of these is crucial, as ratio and proportion are woven deeply into the fabric of our daily activities, from intricate business dealings to the simplicity of preparing a home-cooked meal. When you see fractions presented in the form ‘a:b’, you’re observing a ratio. Conversely, when two such ratios equate, they form a proportion. And these concepts aren’t just restricted to math; they find resonance in science too.

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260+ Most Asked Ratio And Proportion Questions

21. Ratio of three number is 2 : 3 : 1 and their product is 162. Sum of the first two numbers is how much more than the third number?
     
तीन संख्याओं का अनुपात 2 : 3 : 1 है और उनका गुणनफल 162 है। पहली दो संख्याओं का योग, तीसरी संख्या से कितना अधिक है?


Option”C” is correct

Given:

Ratio of three numbers = 2 : 3 : 1

Product of three numbers = 162

Calculation:

Ratio of three numbers = 2x : 3x : x

According to the question

2x × 3x × x = 162

⇒ 6x3 = 162

⇒ x3 = 162/6

⇒ x3 = 27

⇒ x = 3

First number = 2 × 3 = 6

Second number = 3 × 3 = 9

Third number = 3

Sum of first two numbers = 6 + 9 = 15

∴ Sum of first two number is more than the third number = 15 – 3 = 12

22. If a : b : c = 1/2 : 1/3 : 1/5, then find the value of c : b : a

यदि a : b : c = 1/2 : 1/3 : 1/5 है, तो c : b : a का मान ज्ञात कीजिए।


Option”D” is correct

Given:

a : b : c = 1/2 : 1/3 : 1/5

Calculation:

a : b : c

⇒ 1/2 : 1/3 : 1/5

⇒ 30/2 : 30/3 : 30/5 [LCM of 2, 3 and 5 = 30]

⇒ 15 : 10 : 6

Hence,

c : b : a = 6 : 10 : 15 

23. A certain sum was divided among A, B and C in the ratio 5 : 7 : 6. If B received Rs. 4,500 more than C, find C’s share.

एक निश्चित राशि को A, B और C के बीच 5 : 7 : 6. के अनुपात में विभाजित किया जाता है। यदि B का हिस्सा C से 4,500 रूपए अधिक है तो C का हिस्सा ज्ञात कीजिए।


Option”C” is correct

Given:
Ratio of sum divided among A, B And C = 5 : 7 : 6
Share of B – Share of C = Rs. 4500 

Calculation:
Let the share of A, B and C be 5x, 7x and 6x respectively.
⇒ 7x – 6x = 4500
⇒ x = 4500
Share of C = 6x
⇒ 6 × 4500
⇒ 27000
∴ The share of C is 27000.

24. If 7 is added to a number and the initial number is multiplied by 2, then the ratio of both quantities is 3 ∶ 4. Find the initial number.

यदि 7 को एक संख्या में जोड़ा जाता है और प्रारंभिक संख्या को 2 से गुणा किया जाता है, तो दोनों राशियों का अनुपात 3 : 4 है प्रारंभिक संख्या का ज्ञात कीजिये।


Option”B” is correct

Given:

7 added to a number and initial number is multiplied by 2

Ratio of quantities = 3 ∶ 4

Calculation:

Let the initial number be x

7 is added to the number = (x + 7)

2 is multiplied to the number = 2x

Now, the ratio is 3 ∶ 4

(x + 7)/2x = 3/4

⇒ 2x = 28

⇒ x = 14

∴ The initial number is 14

25. If Rs. 25,000 is to be divided between A, B and C in the ratio 1/10 : 1/6 : 1/15, then how much will C get (in Rs)?

यदि 25,000 रुपये को A, B और C के बीच 1/10 : 1/6 : 1/15 के अनुपात में विभाजित किया जाना है, तो C को (रु. में) कितना मिलेगा?


Option”A” is correct

Let the sum received by A, B and C be x/10, x/6 and x/15 respectively

According to the question,

x/10 + x/6 + x/15 = 25000

⇒ 10x/30 = 25000

⇒ x = 75000

∴ C will get = x/15 = 75000/15 = Rs. 5000

26. The ratio of sand to gravel in a mixture is 7 : 8 while that between gravel and cement is 6 : 7. What is the ratio of sand to cement in the mixture?

एक मिश्रण में रेत और बजरी का अनुपात 7 : 8 है जबकि बजरी और सीमेंट का अनुपात 6 : 7 है। मिश्रण में रेत और सीमेंट का अनुपात कितना है?


Option”C” is correct

Given:

The ratio of sand to gravel in a mixture is 7 : 8 while that between gravel and cement is 6 : 7

Calculation:

The ratio of sand to gravel in a mixture is 7 : 8,

⇒ S : G = 7 : 8

While that between gravel and cement is 6 : 7,

⇒ G : C = 6 : 7

⇒ S : C = 42 : 56 = 3 : 4

Therefore, the correct answer is 3 : 4.

27. A sum of Rs. 1,500 was divided between A and B. If 4/5 of what A received was equal to 2/5 of what B received, then what was the amount that B received?

1,500 रुपये की धनराशि को A और B के बीच विभाजित किया जाता है। A को प्राप्त हुआ 4/5 भाग, B के 2/5 भाग के बराबर है, तो B के द्वारा प्राप्त धनराशि क्या थी?


Option”A” is correct

Given:

Total amount = Rs. 1,500

4/5 of amount  A received = 2/5 of amount B received

Calculation:

Let the amount received by A and B be x and y respectively.

According to the question,

⇒ 4/5 of x = 2/5 of y

⇒ x/y = 1/2

⇒ x : y = 1 : 2

⇒ 3 units = 1,500

⇒ 1 unit = 500

⇒ 2 unit = 1,000

∴ The amount that B received was Rs. 1,000.

28. If a : b = 2 : 3 and c : b = 5 : 6, then a : b : c is equal to:

यदि a : b = 2 : 3 और c : b = 5 : 6, तो a : b : c बराबर है:


Option”C” is correct

⇒ a : b = 2 : 3        —-(1)

⇒ c : b = 5 : 6        —-(2)

In both the ratios value of b is different i.e 3 and 6

Hence, we will make b equal in both the ratios

Multiply by 2 in equation (1). we get

a : b = 4 : 6

Now the ratio will become,

a : b = 4 : 6        —-(1)

c : b = 5 : 6

So, 

⇒ a : b : c = 4 : 6 : 5

29. Two numbers are ratio 3 : 4. On increasing each of them by 30, the ratio becomes 9 : 10. The sum of the numbers is:

दो संख्याओं का अनुपात 3 : 4 है। उनमें से प्रत्येक को 30 बढ़ाने पर अनुपात 9 : 10 हो जाता है। तो संख्याओं का योग क्या है?


Option”D” is correct

Let the 1st number be 3x and 2nd number be 4x.

According to question,

(3x + 30)/(4x + 30) = 9/10

⇒ 30 = 6x

⇒ x = 5

Sum of numbers = 3x + 4x = 7x = 7 × 5 = 35

30. The ratio of the present ages of A and B is 6 : 5. Four years ago, the ratio was 5 : 4. What will be the ratio of the ages of A and B after 12 years from now?

A और B की वर्तमान आयु का अनुपात 6 : 5 है। चार वर्ष पहले, अनुपात 5 : 4 था। अब से 12 वर्ष बाद A और B की आयु का अनुपात क्या होगा?


Option”B” is correct

Let the present age of A and B be 6x and 5x

According to question

(6x – 4)/(5x – 4) = 5/4

⇒ 24x – 16 = 25x – 20

⇒ x = 4

∴ Present age of A = 6x = 6 × 4 = 24

And present age of B = 5x = 5 × 4 = 20

After 12 year age of A will be = 24 + 12 = 36 year

And 12 age of B will be = 20 + 12 = 32 year

∴ Required ratio = 36 : 32 = 9 : 8