Quantitative Aptitude

Ratio and Proportion

775 Questions
All Dividing a total in a given ratio 393 Income, expenditure, and equal-savings equations 117 Ratio changes with constant sum/difference 89 Combining ratios 72 Finding a missing term in a proportion 54 Direct, inverse, and power variation 29 Mean proportional 9 Compound, duplicate, and root ratios 8 Componendo and dividendo 2

Ratio and Proportion Questions

Multiple choice

An amount of money is to be divided among Sakshi, Aastha and Ruchita in the ratio of 3 : 5 : 7 respectively. If the amount received by Ruchita is Rs. 8000 more then the amount received by Aastha, what will be the average amount received by Sakshi & Aastha ? किसी निश्चित धनराशि को साक्षी, आस्था और रूचिता में 3: 5: 7 के अनुपात में बांटा जाना है। यदि रूचिता के द्वारा प्राप्त धनराशि आस्था के द्वारा प्राप्त धनराशि से 8000 रू. अधिक है तो साक्षी और आस्था के द्वारा प्राप्त धनराशि का औसत क्या है ?

  1. Rs. 32000

  2. Rs. 20000

  3. Rs. 25000

  4. Rs. 16000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let amounts be 3x, 5x, 7x. Ruchita gets 8000 more than Aastha: 7x - 5x = 2x = 8000, so x = 4000. Sakshi = 3(4000) = 12000, Aastha = 5(4000) = 20000. Average of Sakshi and Aastha = (12000 + 20000)/2 = 16000. Option A (Rs. 32000) is the sum, not the average.

Multiple choice

Annual incomes of Amit and Veeri are in the ratio 3:2, while the ratio of their expenditure is 5:3. If at the end of the year each saves Rs 1000, the annual income of Amit is - अमित तथा वीरी की वार्षिक आय 3 : 2 के अनुपात में हैं, जबकि उनका खर्च 5 : 3 के अनुपात में है। तदनुसार, यदि उनमें, प्रत्येक की वर्ष के अंत में बचत रू 1000 हो, तो अमित की वार्षिक आय कितनी है?

  1. Rs 9000

  2. Rs 8000

  3. Rs 7000

  4. Rs 6000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Amit's income = 3x, Veeri's income = 2x. Amit's expenditure = 5y, Veeri's expenditure = 3y. Savings = Income - Expenditure. For both: 3x - 5y = 1000 and 2x - 3y = 1000. Solving: From second equation, 2x = 1000 + 3y, so x = 500 + 1.5y. Substituting in first: 3(500 + 1.5y) - 5y = 1000, giving 1500 + 4.5y - 5y = 1000, so -0.5y = -500, y = 1000. Then x = 500 + 1500 = 2000. Amit's income = 3x = 3 × 2000 = Rs 6000. Option A (9000) uses incorrect ratio values.

Multiple choice

Rs. 33,630 are divided among A, B and C in such a manner that the ratio of the amount of A to that of B is 3:7 and the ratio of the amount B to that of C is 6:5. The amount of money received by B is - 33,630 रू. को A, B और C में इस प्रकार विभाजित करना है कि A की धनराशि का B से अनुपात 3:7 है और B की धनराशि का C से अनुपात 6:5 है। B द्वारा प्राप्त धनराशि है-

  1. 14686

  2. 14868

  3. 15886

  4. 14786
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find B's share, first combine the ratios A:B = 3:7 and B:C = 6:5. Make B consistent by taking LCM of 7 and 6 = 42. This gives A:B:C = 18:42:35. Total parts = 95, so B receives (42/95) × 33630 = 14868.

Multiple choice

The respective ratio of monthly income of Polly,Samiksha and Vipul is 84 : 67 : 89 respectively.If Samiksha 's annual income is Rs.120600 then what is the sum of annual income of Polly and Vipul?

  1. Rs. 348200

  2. Rs.311400

  3. Rs. 302800

  4. Rs.322600

  5. Rs.362600
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Samiksha's monthly income = 120600/12 = Rs. 10,050. The ratio 84:67:89 means if 67x = 10050, then x = 10050/67 = 150. Polly's monthly = 84×150 = 12600, annual = 12600×12 = 151200. Vipul's monthly = 89×150 = 13350, annual = 13350×12 = 160200. Sum = 151200 + 160200 = 311400. Option B matches.

Multiple choice

A, B and C divide an amount of Rs 9,915 amongst themselves in the ratio 3 : 5 : 7 respectively.What is the C's share in the amount? A, B तथा C रू. 9, 915 की धनराशि को आपस में क्रमशः 3 : 5 : 7 के अनुपात में बाँटते है। धनराशि में C का हिस्सा क्या है?

  1. ₹4627

  2. ₹1267

  3. ₹4267

  4. ₹3127
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

C's share is calculated as 7/15 of Rs 9,915 (total ratio parts = 3+5+7=15). 7/15 × 9915 = 7 × 661 = Rs 4,627. Option B (1267) is A's share (3/15), Option C (4267) is a transposition error, and Option D (3127) is B's share (5/15).

Multiple choice

The ratio of income of Anil and Mukesh is 2 : 3. The sum of their expenditure is Rs. 8000 and the amount of saving of Anil is equal to amount of expenditure of Mukesh. What is the sum of their saving ? अनिल और मुकेश की आय का अनुपात 2 : 3 है। उनके खर्चों का योग 8000 रू. है और अनिल की बचत की धनराशि मुकेश के खर्चे के बराबर है। उनकी बचतों का योग क्या है ?

  1. 22000

  2. 4000

  3. 16000

  4. 12000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Anil's income be 2x, Mukesh's be 3x. Given expenditure sum = 8000, and Anil's savings = Mukesh's expenditure. Let Anil's expenditure = Ea, savings = Sa. Mukesh's expenditure = Em, savings = Sm. We have: Ea + Em = 8000, and Sa = Em. Also: 2x = Ea + Sa, 3x = Em + Sm. Substituting Sa = Em: 2x = Ea + Em, 3x = Em + Sm. From Ea + Em = 8000, we get 2x = 8000, so x = 4000. Total savings = Sa + Sm = Em + (3x - Em) = 3x = 12000.

Multiple choice

An employer reduces the number of his employees in the ratio of 8 : 7 and increases their wages in the ratio of 15 : 16. If the original wage bill was Rs. 16400. Find the ratio in which the wage bill is decreased. एक नियोक्ता अपने कर्मचारियों की संख्या 8 : 7 के अनुपात में घटाता है, और उनका वेतन 15 : 16. के अनुपात में बढ़ाता है। यदि प्रारम्भिक वेतन बिल रू.16400 था, तो वेतन बिल किस अनुपात में कम हुआ?

  1. 15 : 14

  2. 17 : 19

  3. 21 : 20

  4. 20 : 21
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original wage bill = employees × wage = 8 × 15 = 120 units. New wage bill = 7 × 16 = 112 units. Ratio decrease = 120:112 = 15:14 (dividing by 8). The original wage bill of Rs. 16400 is extra information not needed for the ratio. Option A is correct.

Multiple choice

Salaries of A and B are in the ratio of 13 : 7 respectively . If A’s salary is increased by 25%, then it will become Rs. 16250 What is B’s salary ? A और B के वेतन का अनुपात क्रमश: 13 : 7 है। यदि A के वेतन में 25% की वृद्धि की जाती है, तो वह बढ़कर 16250 रू. हो जाती है । B का वेतन क्या है ?

  1. 1400

  2. 14000

  3. 7000

  4. 10000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A's original salary be 13x and B's be 7x. After 25% increase, A's salary is 1.25 × 13x = 16.25x = 16250. So x = 1000 and B's salary = 7x = 7000. Options A and B have calculation errors, while D doesn't follow the ratio.

Multiple choice

A bag contains 50 paisa Rs. 1 and Rs. 2 coins in the ratio 2 : 3 : 4. If the total amount is Rs. 240 what is the total number of coins. एक बैग में 50 पैसे रू.1 और रू. 2 के सिक्के 2 : 3 : 4 के अनुपात में है। यदि कुल राशि 240 रू. है। कुल सिक्कों की संख्या कितनी है?

  1. 200

  2. 150

  3. 180

  4. 90
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let coins be 2x, 3x, 4x of 50 paisa, Rs. 1, and Rs. 2 respectively. Total value = 2x(0.5) + 3x(1) + 4x(2) = x + 3x + 8x = 12x = Rs. 240. So x = 20. Total coins = 2x + 3x + 4x = 9x = 9 × 20 = 180 coins.

Multiple choice

The ratio between the monthly income of A, B and C is 2 : 3 : 5. If C's monthly income is Rs. 1500 more than the A's monthly income, then find the B's annual income. A, B और C की मासिक आय का अनुपात 2 : 3 : 5 है | यदि C की मासिक आय A की मासिक आय से रु 1500 अधिक है, तो B की वार्षिक आय ज्ञात कीजिये |

  1. Rs./रु 30000

  2. Rs./रु18000

  3. Rs./रु 1500

  4. Rs./रु 20000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let monthly incomes of A, B, C be 2x, 3x, 5x respectively. Given C's monthly income exceeds A's by Rs. 1500: 5x - 2x = 1500, so 3x = 1500, which means x = 500. B's monthly income = 3x = 3 × 500 = Rs. 1500. B's annual income = 1500 × 12 = Rs. 18,000. Note: Option C shows Rs. 1500, which is B's monthly income, not annual - this is a distractor.

Multiple choice

The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is संख्याओं का योग 98 है यदि प्रथम और दूसरी का अनुपात 2 : 3 और दूसरी और तीसरी का अनुपात 5 : 8 है तो दूसरी संख्या है-

  1. 20

  2. 30

  3. 38

  4. 48
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given first:second = 2:3 and second:third = 5:8. To combine, make second terms equal: 2:3 = 10:15. So first:second:third = 10:15:24. Total parts = 49. Each part = 98/49 = 2. Second number = 15 × 2 = 30.

Multiple choice

If 30% of a number is equal to two third of another number, what is the ratio of the first number to the second? यदि किसी संख्या का 30% दूसरी संख्या के 2/3 के बराबर है, तो दोनों संख्याओं के अनुपात क्या हैं?

  1. 1 : 9

  2. 1 : 3

  3. 20 : 9

  4. 9 : 20
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the first number be x and second be y. 30% of x = 2/3 of y, so 0.3x = 2y/3. Solving: x/y = (2/3)/0.3 = (2/3)/(3/10) = 20/9. The ratio is 20:9.