Ratio and Proportion Questions with Solutions | Ratio and Proportion Aptitude Questions with Solutions

1

In the income statement of Asha and Ravenna, the ratio of their income in the year 2017 was 5 : 4. The ratio of Asha’s income in the year 2018 to that in 2017 is 3 : 5 and the ratio of Ravenna’s income in the year 2018 to that in 2017 is 3 : 2. If Rs. 10242 is the sum of the income of Asha and Ravenna in the year 2018, then find the income of Ravenna in the year 2017?

» Explain it

Correct Option: E

Let the income of Asha in 2018 and 2017 be 3x and 5x respectively.

Let the income of Ravenna in 2018 and 2017 be 3y and 2y respectively

Since, the ratio of their income in the year 2017 was 5 : 4

5x : 2y = 5 : 4

2x = y

The sum of their incomes in 2018 is Rs. 10242

3x + 3y = 10, 242

9x = 10, 242

x = 1,138 and y = 2276

Ravenna’s income for the year 2017 = 2y = Rs. 4552

Hence, option E is correct.

1

आशा और रवेना के आय विवरण में, वर्ष 2017 में उनकी आय का अनुपात 5 : 4 था। वर्ष 2018 में आशा की आय का 2017 में अनुपात 3 : 5 है और वर्ष 2018 में रवेना की आय का 2017 में अनुपात 3:2 है। यदि वर्ष 2018 में 10242 रुपये आशा और रवेना की आय का योग है, तो वर्ष 2017 में रवेना की आय ज्ञात कीजिये?

» Explain it

सही विकल्प : E

Let the income of Asha in 2018 and 2017 be 3x and 5x respectively.

Let the income of Ravenna in 2018 and 2017 be 3y and 2y respectively

Since, the ratio of their income in the year 2017 was 5 : 4

5x : 2y = 5 : 4

2x = y

The sum of their incomes in 2018 is Rs. 10242

3x + 3y = 10, 242

9x = 10, 242

x = 1,138 and y = 2276

Ravenna’s income for the year 2017 = 2y = Rs. 4552

Hence, option E is correct.

2

Two vessels A and B of equal volume contain milk and water in the ratio 3 : 2 and 2 : 1 to their brim respectively. Two litres of the solution from vessel A and three litres of the solution from vessel B are poured into a big empty vessel C. If the solution in C occupied 40% of the capacity of C, what proportion of the volume of vessel C should be the volume of water that shall be added so that the ratio of milk and water in vessel C becomes 1 : 1?

» Explain it

Correct Option: D

Amount of milk poured into C from vessel A and B

= 2 ×	3	+ 3 ×	2	=	16	litres
	5		3		5

Also, amount of water poured into C from vessels A and B

= 5 –	16	=	9	litres
	5		5

Given, 5 litres represent 40% of the capacity of vessel C, vessel C has a capacity of

= 5 ×	5	= 12.5 litres
	2

To make the quantities of water and milk same in the vessel C, quantity of water to be added

=	16	–	9	=	7	litres
	5		5		5

Therefore, reqd. answer =	7/5	=	14
	12.5		125

Hence, option D is correct.

2

समान मात्रा के दो पात्र A और B में क्रमशः 3: 2 और 2: 1 के अनुपात में दूध और पानी है। पात्र A से विलयन के दो लीटर और पात्र B से विलयन के तीन लीटर को एक बड़े खाली पात्र C में डाला जाता है। यदि विलयन पात्र C में 40% जगह घेर लेता है, तो पात्र C कितनी मात्रा में पानी डाला जाये ताकि पात्र में दूध और पानी का अनुपात 1: 1 हो जाए?

» Explain it

सही विकल्प : D

Amount of milk poured into C from vessel A and B

= 2 ×	3	+ 3 ×	2	=	16	litres
	5		3		5

Also, amount of water poured into C from vessels A and B

= 5 –	16	=	9	litres
	5		5

Given, 5 litres represent 40% of the capacity of vessel C, vessel C has a capacity of

= 5 ×	5	= 12.5 litres
	2

To make the quantities of water and milk same in the vessel C, quantity of water to be added

=	16	–	9	=	7	litres
	5		5		5

Therefore, reqd. answer =	7/5	=	14
	12.5		125

Hence, option D is correct.

3

The average score in an examination taken by 52 students of a class is 85. If the scores of the best 5 performers are not considered, the average score of the remaining students falls by 2. If, none of the first five highest scorers is not below 80 and if each of the 5 top scorers had distinct integral scores, find the maximum possible score of the topper.

» Explain it

Correct Option: D

Let the score of the topper be T.

Total score of the 52 students = 52 × 85 = 4420

Total score of the remaining 47 students after scores of the best five performers are removed = 47 × 83 = 3901

Total score of the top five students = 4420 – 3901 = 519

T + (total score of the next 4 top scores) = 519

T is the maximum when the total score of the next 4 top scorers is minimum.

Total score of the next 4 top scorers has a minimum value of 80 + 81 + 82 + 83 = 326 (since all the top 5 scores are distinct) and the least is 80.

T has a maximum value of 519 – 326 = 193

Hence, option D is correct.

3

एक कक्षा के 52 छात्रों द्वारा ली गई परीक्षा में औसत अंक 85 है। यदि सर्वश्रेष्ठ 5 कलाकारों के अंकों पर विचार नहीं किया जाता है, तो शेष छात्रों का औसत स्कोर 2 से गिर जाता है। यदि पहले पांच उच्चतम छात्रों में से कोई भी 80 से नीचे नहीं है, और यदि 5 शीर्ष छात्रों में से प्रत्येक के अलग-अलग अभिन्न अंक थे, तो टॉपर का अधिकतम संभव अंक ज्ञात करें।

» Explain it

सही विकल्प : D

Let the score of the topper be T.

Total score of the 52 students = 52 × 85 = 4420

Total score of the remaining 47 students after scores of the best five performers are removed = 47 × 83 = 3901

Total score of the top five students = 4420 – 3901 = 519

T + (total score of the next 4 top scores) = 519

T is the maximum when the total score of the next 4 top scorers is minimum.

Total score of the next 4 top scorers has a minimum value of 80 + 81 + 82 + 83 = 326 (since all the top 5 scores are distinct) and the least is 80.

T has a maximum value of 519 – 326 = 193

Hence, option D is correct.

4

A bag contains certain number of coins of different denominations. The ratio of the number of Rs. 1 coins to Rs. 2 coins is 5 : 7, respectively and the ratio of number of Rs. 2 coins to Rs. 5 coins is 7 : 6 respectively. Find the total value of the Rs. 5 coins, if the total value of the Rs. 1 coins in the bag is Rs. 15.

» Explain it

Correct Option: B

Ratio of the number of coins of denominations Rs. 1 : Rs. 2 : Rs. 5 = 5 : 7 : 6

Let, the number of coins of Rs. 1, Rs. 2 and Rs. 5 in the bag be 5x, 7x and 6x.

Since, the total value of Rs. 1 coin in the bag is Rs. 15

So, the number of coins of Rs. 1 in a bag = 15

5x = 15 , ⇒ x = 3

Therefore, number of Rs. 5 coins in the bag = 6x = 18

So, required value of Rs. 5 coins = 6 × 3 × 5 = Rs.90

Hence, option B is correct.

4

एक बैग में विभिन्न संप्रदायों के सिक्कों की निश्चित संख्या है। 1 रुपये के सिक्के की संख्या और 2 रुपये के सिक्के की संख्या का अनुपात क्रमशः 5 : 7 हैं, और 2 रुपये के सिक्के की संख्या और 5 रुपये के सिक्के की संख्या का अनुपात क्रमशः 7 : 6 हैं। 5 रुपये के सिक्कों का कुल मान ज्ञात कीजिए। अगर 1 रुपये के सिक्कों का कुल मान 15 रुपये है।

» Explain it

सही विकल्प : B

Ratio of the number of coins of denominations Rs. 1 : Rs. 2 : Rs. 5 = 5 : 7 : 6

Let, the number of coins of Rs. 1, Rs. 2 and Rs. 5 in the bag be 5x, 7x and 6x.

Since, the total value of Rs. 1 coin in the bag is Rs. 15

So, the number of coins of Rs. 1 in a bag = 15

5x = 15 , ⇒ x = 3

Therefore, number of Rs. 5 coins in the bag = 6x = 18

So, required value of Rs. 5 coins = 6 × 3 × 5 = Rs.90

Hence, option B is correct.

5

A father distributed some chocolates among his four children and kept some with him. The eldest three children got chocolates in the ratio 3 : 11 : 7. The total number of chocolates with father and youngest child is three times the total chocolates with the three eldest children. The ratio of chocolates with father and that with all the children is 3 : 4. Find the total number of chocolates if the youngest child has 81 chocolates with him?

» Explain it

Correct Option: B

Let the children be P, Q, R and S and Father be F

Chocolates with P : Q : R= 3 : 7 : 11

Let the number of chocolates be 3k, 7k and 11k

Total chocolates with three eldest children = 21k

Chocolate with F and S = 3 × 21k = 63k

Total chocolates = (21k + 63k) = 84k

Chocolate with F : (P + Q + R + S) = 3 : 4

Total 7 units of chocolate = 84 k

1 unit = 12k

Chocolate with F = 3 × 12k = 36k

Chocolate with S = (63k – 36k) = 27k

27 k = 81 → k=3

Total number of chocolates = 84k = 84 × 3 = 252

Hence, option B is correct.

5

एक पिता ने अपने चार बच्चों के बीच कुछ चॉकलेट बांटे और कुछ अपने पास रखे। 3 : 11 : 7 अनुपात में सबसे बड़े तीन बच्चों को चॉकलेट मिली। पिता और सबसे छोटे बच्चे के पास चॉकलेट की कुल संख्या तीन बड़े बच्चों के पास कुल चॉकलेट का तीन गुना है। पिता के पास और सभी बच्चों के पास चॉकलेट का अनुपात 3 : 4 है। यदि सबसे छोटे बच्चे के पास 81 चॉकलेट हैं, तो चॉकलेट की कुल संख्या ज्ञात करें?

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सही विकल्प : B