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

101. If a + b + c = 27 and a + b ∶ b + c ∶ c + a = 7 ∶ 6 ∶ 5, find the value of 1/a ∶ 1/b ∶ 1/c.
यदि a + b + c = 27 तथा a + b ∶ b + c ∶ c + a = 7 ∶ 6 ∶ 5 हो, तो 1/a ∶ 1/b ∶ 1/c का मान ज्ञात कीजिये

3 ∶ 4 ∶ 2
4 ∶ 3 ∶ 6
5 ∶ 4 ∶ 3
7 ∶ 6 ∶ 5

Option”B” is correct

Given, (a + b + c) = 27

⇒ (a + b) : (b + c) : (c + a) = 7x : 6x : 5x

⇒ 2(a + b + c) = 7x + 6x + 5x = 18x

⇒ (a + b + c) = 9x

⇒ 9x = 27

⇒ x = 3

⇒ a + b = 7x = 7 × 3 = 21

⇒ c = 27 – 21 = 6

⇒ b + c = 6x = 6 × 3 = 18

⇒ b = 18 – 6 = 12

⇒ a = 9

⇒ 1/a : 1/b : 1/c

⇒ 1/9 : 1/12 : 1/6

Multiply by 36

⇒ 36/9 : 36/12 : 36/6 = 4 : 3 : 6

102. Two numbers are in the ratio 18 ∶ 35. Half of the smaller number is greater than one fifth of the greater by 6. What is the smaller number?
दो संख्याएँ 18 ∶ 35 के अनुपात में हैं। छोटी संख्या का आधा भाग बड़ी संख्या के पाँचवे भाग से 6 अधिक है। छोटी संख्या क्या है?

Option”B” is correct

Let the smaller number be 18x and the greater number = 35x

According to problem,

⇒ 18x × 1/2 = 35x × 1/5 + 6

⇒ 9x = 7x + 6

⇒ x = 3

∴ The smaller number = 18 × 3 = 54

103. A, B and C are partners in a firm sharing profit in the ratio of 3 ∶ 4 ∶ 5. If they set aside 4% of the profits as emergency fund and shared the rest of the profit and B gets his share of profit as Rs. 1, 81, 400, the amount of profit set aside for emergency fund is∶
A, B और C एक कंपनी में 3 ∶ 4 ∶ 5 के अनुपात में लाभ साझा करने वाले साझेदार हैं। यदि वे लाभ के 4% को आपातकालीन निधि के रूप में अलग रख देते हैं और शेष लाभ को बाँट लेते हैं और B, 1, 81, 400 रुपए के रूप में लाभ का उसका हिस्सा प्राप्त करता है, तो आपातकालीन निधि के लिए अलग रखे गए लाभ की राशि क्या है?

Rs. 27, 845
Rs. 18, 140
Rs. 22, 675
Rs. 24, 500

Option”C” is correct

Let the total profit is P.

Profit remains after emergency fund = 96% of P

Total share = 3 + 4 + 5 = 12

Share of B = (4/12) × (96/100) × P = Rs. 181400

⇒ P = Rs. 566875

∴ Emergency fund = (4/100) × 566875 = Rs. 22675

104. There are 60 bins for red colour and some blue bins in a box. The number of blue bins is 10 less than half the number of red bins. The sum and difference between the price of a red bin and the price of a blue bin are Rs. 220 and Rs. 20 respectively. Find the ratio of total money of red bins to blue bins he get after selling the bins box. Given that the price of a red bin is higher than a blue bin.
एक बॉक्स में लाल रंग के 60 डिब्बे और कुछ नीले रंग के डिब्बे हैं। नीले डिब्बों की संख्या, लाल डिब्बों की संख्या के आधे से 10 कम है। एक लाल डिब्बे और एक नीले डिब्बे के मूल्य का योगफल और अंतर क्रमशः 220 रुपये और 20 रुपये है। लाल डिब्बों और नीले डिब्बों को बेचने पर प्राप्त कुल धनराशि का अनुपात ज्ञात कीजिए। यह दिया है कि एक लाल डिब्बे की कीमत एक नीले डिब्बे से अधिक है।

18 ∶ 5
5 ∶ 18
5 ∶ 2
2 ∶ 5

Option”A” is correct

Let the number of red bins and blue bins be m and n respectively,

⇒ m = 60

⇒ n = 60/2 – 10 = 20

Ratio of number of red and blue bins = 60 ∶ 20 = 3 ∶ 1

Let the price of one red bin and the price of one blue bin be Rs.a and Rs.b respectively,

⇒ a + b = 220

⇒ a – b = 20

Solving,

⇒ a = 120

⇒ b = 100

The ratio of the price of a red bin and the price of a blue bin = 120 ∶ 100 = 6 ∶ 5

The ratio of total money gets after selling the box = compound ratio

= (3 ∶ 1) and (6 ∶ 5)

= (3 × 6) ∶ (1 × 5)

= 18 ∶ 5

105. If the compound ratio of ratios (x ∶ 2) and (9 ∶ y) is 3 ∶ 4, then find the compound ratio of ratios (x + y) ∶ 5 and 2 ∶ y.
यदि अनुपात (x ∶ 2) और (9 ∶ y) का मिश्र अनुपात 3 ∶ 4 है, तो अनुपात (x + y) ∶ 5 और 2 ∶ y का मिश्र अनुपात ज्ञात कीजिये।

3 ∶ 20
7 ∶ 15
9 ∶ 10
2 ∶ 5

Option”B” is correct

The compound ratio of ratios a ∶ b and c ∶ d is ac ∶ bd.

⇒ 9x ∶ 2y = 3 ∶ 4

⇒ x/y = 2/9 × 3/4

⇒ x/y = 1/6 —-(1)

Similarly,

Compound ratio of ratios (x + y) ∶ 5 and 2 ∶ y = 2/5 × (x + y)/y = 2/5 × (x/y + 1)

Substituting from (1),

⇒ Compound ratio of ratios (x + y) ∶ 5 and 2 ∶ y = 2/5 × (1/6 + 1) = 2/5 × 7/6 = 7/15

∴ Compound ratio of ratios (x + y) ∶ 5 and 2 ∶ y = 7 ∶ 15

106. The ratio of monthly incomes of A and B is 3 : 4 and the ratio of their monthly savings is 7 : 6, If the income of A is equal to twice the expenditure of B, then what is the ratio of the expenditures of A and B?
A और B की मासिक आय का अनुपात 3 : 4 है और उनकी मासिक बचत का अनुपात 7 : 6 है, यदि A की आय B के व्यय के दोगुने के बराबर है, तो A और B के व्यय का अनुपात क्या है?

2 : 1
3 : 5
2 : 3
1 : 18

Option”D” is correct

Ratio of monthly income of A and B is 3 : 4

Ratio of monthly savings of A and B is 7 : 6

Income of A = 2 × Expenditure of B

Concept used:

Savings = Income – Expenditure

Calculation:

Let the monthly incomes of A and B are 3x and 4x

Their monthly savings are 7y and 6y

According to the question

3x = 2 × (4x – 6y)

⇒ 3x = 8x – 12y

⇒ 8x – 3x = 12y

⇒ 5x = 12y

⇒ x : y = 12 : 5

Income of A = 3x = 3 × 12 = 36

Income of B = 4x = 4 × 12 = 48

Savings of A = 7y = 7 × 5 = 35

Savings of B = 6y = 6 × 5 = 30

Expenditure of A = 36 – 35 = 1

Expenditure of B = 48 – 30 = 18

The ratio of expenditure of A to than that of B is 1 : 18

107. Find the value of $(\frac{p^{2} + q^{2}}{r^{2} + s^{2}})$ , if p ∶ q ∶∶ r ∶ s.
$(\frac{p^{2} + q^{2}}{r^{2} + s^{2}})$ का मान ज्ञात कीजिए, यदि p ∶ q ∶∶ r ∶ s है.

q2s2
r2s2
p2q2
None of these

Option”A” is correct

Given:

p ∶ q ∶∶ r ∶ s

Calculation:

⇒ $\frac{p}{q}$ = $\frac{r}{s}$

By squaring both sides

⇒ $\frac{p^{2}}{q^{2}}$ = $\frac{r^{2}}{s^{2}}$

Now, Adding 1 on both sides

⇒ $\frac{p^{2}}{q^{2}}$ + 1 = $\frac{r^{2}}{s^{2}}$ + 1

⇒ $\frac{p^{2} + q^{2}}{q^{2}} = \frac{r^{2} + s^{2}}{s^{2}}$

∴ $\frac{p^{2} + q^{2}}{r^{2} + s^{2}} = \frac{q^{2}}{s^{2}}$

108. In a class, 20% of the boys have blue eyes and 10% of the girl has blue eyes. If the ratio of boys to girls in the class is 4:3, then what is the proportion of the students in the class having blue eyes?
एक कक्षा में 20% लड़कों की आँखे नीली हैं और 10% लड़कियों की आँखे नीली हैं। यदि कक्षा में लड़कों और लड़कियों का अनुपात 4:3 है, तो कक्षा में नीली आँख वाले छात्रों का अनुपात क्या है?

12/33
12/45
11/45
11/70

Option”D” is correct

Ratio of boys to girls in the class = 4 : 3 or 40x : 30x

Total number of students in the class = 40 + 30 = 70x

Number of boys who has blue eyes = 40x × (20/100)= 8x

Number of girls who has blue eyes = 30x × (10/100) = 3x

Total number of students who has blue eyes = 8x + 3x = 11x

The proportion of the students in the class having blue eyes = 11x/70x = 11/70

109. If compound ratio of 9 : 5 and 4 : 5 is x : y, then mean proportion of x and y is:
यदि 9 : 5 और 4 : 5 का यौगिक अनुपात x : y है, तो x और y का मध्यानुपाती है:

Option”A” is correct

Compound ratio of 9 : 5 and 4 : 5 is x : y

Concept:/Formula:

Mean proportion of x and y is = √xy

Compound proportion of a : b and c : d = ac : bd

Calculation:

Compound ratio of 9 : 5 and 4 : 5 is = (9 × 4) : (5 × 5) = 36 : 25

⇒ x : y = 36 : 25

⇒ x = 36 and y = 25

Mean proportion of x and y = √(25 × 36) = 5 × 6 = 30

110. A person gave 2/7^th of his income to his wife and 3/11^th to his son. The remaining income was invested in three trusts A, B, and C in the ratio 4: 6: 7. The difference in the amount received by the wife and son is Rs. 300. How much of the money is saved in trust B?
एक व्यक्ति अपनी आय के 2/7वें हिस्से को अपनी पत्नी को देता है, 3/11वें हिस्से को अपने पुत्र को देता है। शेष आय को वह तीन ट्रस्टों A, B और C में 4 : 6 : 7 के अनुपात में निवेश कर देता है। पत्नी और पुत्र को प्राप्त धनराशि में अंतर 300 रुपए है। ट्रस्ट B में कितनी धनराशि निवेश की गई है?

Rs. 800
Rs. 1200
Rs. 3600
Rs. 2400

Option”C” is correct

A person gave 2/7^th of his income to his wife and 3/11^th to his son. The remaining income was invested in three trusts A, B, and C in the ratio 4: 6: 7.

The difference in the amount received by the wife and son is Rs. 300.

CONCEPT:

Basic ratio concept.

CALCULATION:

Suppose the income of the person = Rs. X

So,

Amount received by the wife = 2X/7

Amount received by the son = 3X/11

Now,

(2X/7) – (3X/11) = 300

⇒ X/77 = 300

⇒ X = 23100

Hence,

Total amount of money invested in three trusts A, B and C

= 23100 – (2 × 23100)/7 – (3 × 23100)/11

= 23100 – 6600 – 6300

= Rs. 10200

Given that this amount is invested in A, B, and C in the ratio 4: 6: 7.

Hence,

Amount invested in trust B = (6/17) × 10200 = Rs. 3600

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