Question 1

The ratio of the present ages of Arun and Bhavna is 5:3. If Arun is 20 years older than Bhavna, what is Bhavna's present age?

Accepted Answer

Step 1: Let Arun's age = 5x and Bhavna's age = 3x (from ratio 5:3). Step 2: Given that Arun is 20 years older than Bhavna, so 5x - 3x = 20. Step 3: 2x = 20, therefore x = 10. Step 4: Bhavna's age = 3x = 3(10) = 30 years.

Question 2

The ratio of the present ages of Arun and Bhavna is 5:3. If Arun is 10 years older than Bhavna, what will be the ratio of their ages after 6 years?

Accepted Answer

Step 1: Let Arun's present age = 5x and Bhavna's present age = 3x. Step 2: Given that Arun is 10 years older than Bhavna, so 5x - 3x = 10, which gives 2x = 10, therefore x = 5. Step 3: Arun's present age = 5(5) = 25 years and Bhavna's present age = 3(5) = 15 years. Step 4: After 6 years, Arun's age = 25 + 6 = 31 years and Bhavna's age = 15 + 6 = 21 years. Step 5: Ratio after 6 years = 31:21. Therefore, the answer is 31:21.

Question 3

If 12 books cost ₹480, what is the cost of 18 books?

Accepted Answer

Step 1: Cost of 1 book = 480 ÷ 12 = ₹40. Step 2: Cost of 18 books = 18 × 40 = ₹720.

Question 4

The ratio of the ages of Ram and Shyam is 3:5. If Ram is 18 years old, what is the age of Shyam?

Accepted Answer

Step 1: Let Ram's age = 3x and Shyam's age = 5x. Step 2: Given Ram's age = 18, so 3x = 18, which gives x = 6. Step 3: Shyam's age = 5x = 5 × 6 = 30 years. Therefore, the answer is 30 years.

Question 5

The ratio of two numbers is 4 : 7. If their difference is 45, find the larger number.

Accepted Answer

Step 1: Let the two numbers be 4x and 7x. Step 2: Their difference is 7x − 4x = 3x. Step 3: Given that 3x = 45, so x = 15. Step 4: The larger number is 7x = 7 × 15 = 105.

Question 6

A shopkeeper mixes two types of rice costing ₹40 per kg and ₹60 per kg in the ratio 3:2. At what price per kg should he sell the mixture to gain 25% profit?

Accepted Answer

Step 1: Let quantities be 3x kg and 2x kg respectively. Step 2: Cost of first type = 3x × 40 = ₹120x. Cost of second type = 2x × 60 = ₹120x. Step 3: Total cost = 120x + 120x = ₹240x. Total quantity = 3x + 2x = 5x kg. Step 4: Cost price per kg = 240x / 5x = ₹48 per kg. Step 5: For 25% profit, selling price = 48 × (1 + 25/100) = 48 × 1.25 = ₹60 per kg.

Question 7

Two alloys contain copper in the percentages 30% and 50% respectively. In what ratio should they be mixed to get an alloy with 40% copper?

Accepted Answer

Step 1: Use alligation method. Alloy 1 has 30% copper, Alloy 2 has 50% copper. Target is 40% copper. Step 2: Difference between Alloy 2 and target = 50 - 40 = 10. Step 3: Difference between target and Alloy 1 = 40 - 30 = 10. Step 4: Ratio = (Alloy 1):(Alloy 2) = 10:10 = 1:1.

Question 8

A shopkeeper mixes two types of rice costing ₹40 per kg and ₹60 per kg in the ratio 3:2. What is the cost price of the mixture per kg?

Accepted Answer

Step 1: Rice type 1 costs ₹40/kg in ratio 3 parts. Rice type 2 costs ₹60/kg in ratio 2 parts. Step 2: Total parts = 3 + 2 = 5. Step 3: Cost of 3 parts of type 1 = 3 × 40 = ₹120. Step 4: Cost of 2 parts of type 2 = 2 × 60 = ₹120. Step 5: Total cost = 120 + 120 = ₹240 for 5 parts. Step 6: Cost per kg = 240 ÷ 5 = ₹48/kg.

Question 9

Vikram's age is 3 years more than twice Isha's age. If Vikram is currently 21 years old, what is Isha's current age?

Accepted Answer

Step 1: Let Isha's current age = x years. Step 2: Vikram's age = 2x + 3 years. Step 3: Given Vikram's age = 21, so 2x + 3 = 21. Step 4: 2x = 21 - 3 = 18. Step 5: x = 18 ÷ 2 = 9. Step 6: Isha's current age = 9 years.

Question 10

The ratio of Ravi's age to Sita's age is 7:5. After 6 years, their ages will be in the ratio 4:3. What is Ravi's current age?

Accepted Answer

Step 1: Let Ravi's current age = 7x and Sita's current age = 5x (from ratio 7:5). Step 2: After 6 years, Ravi's age = 7x + 6 and Sita's age = 5x + 6. Step 3: Given that after 6 years the ratio is 4:3, so (7x + 6)/(5x + 6) = 4/3. Step 4: Cross-multiply: 3(7x + 6) = 4(5x + 6). Step 5: 21x + 18 = 20x + 24. Step 6: 21x - 20x = 24 - 18. Step 7: x = 6. Step 8: Ravi's current age = 7x = 7(6) = 42 years.

Question 11

The ratio of ages of A and B is 3 : 4. If A is 18 years old, how old is B?

Accepted Answer

Step 1: A : B = 3 : 4. Step 2: A's age = 18 years. Step 3: Let A's age = 3x and B's age = 4x. Step 4: 3x = 18, so x = 6. Step 5: B's age = 4x = 4 × 6 = 24 years.

Question 12

A container has milk and water in the ratio 3:1. How much water must be added to 40 litres of this mixture to make the ratio 2:1?

Accepted Answer

Step 1: In 40 litres, milk = 40 × 3/4 = 30 litres, water = 40 × 1/4 = 10 litres. Step 2: Let x litres of water be added. New ratio: 30/(10 + x) = 2/1. Step 3: 30 = 2(10 + x) → 30 = 20 + 2x → 2x = 10 → x = 5. Therefore, 5 litres of water must be added.

Question 13

If A : B = 3 : 5 and B : C = 2 : 3, find A : B : C.

Accepted Answer

Step 1: A : B = 3 : 5 means A/B = 3/5. Step 2: B : C = 2 : 3 means B/C = 2/3. Step 3: To combine, make B the same in both ratios. LCM(5, 2) = 10. Step 4: A : B = 3 : 5 = 6 : 10 (multiply by 2). Step 5: B : C = 2 : 3 = 10 : 15 (multiply by 5). Step 6: Therefore A : B : C = 6 : 10 : 15.

Question 14

The ratio of two numbers is 3:5. If each number is increased by 10, the new ratio becomes 5:7. What is the smaller of the two original numbers?

Accepted Answer

Step 1: Let the two numbers be 3x and 5x. Step 2: After adding 10 to each: (3x + 10)/(5x + 10) = 5/7. Step 3: Cross multiply: 7(3x + 10) = 5(5x + 10) → 21x + 70 = 25x + 50 → 4x = 20 → x = 5. Step 4: The two numbers are 3×5 = 15 and 5×5 = 25. Therefore, the smaller number is 15.

Question 15

Two numbers are in the ratio 7:4. If their difference is 45, what is the larger number?

Accepted Answer

Step 1: Let the numbers be 7x and 4x. Step 2: Their difference = 7x − 4x = 3x = 45. Step 3: x = 15. Step 4: Larger number = 7x = 7 × 15 = 105.

Question 16

Meera's age is 4 times Neha's age. After 8 years, Meera's age will be 2 times Neha's age. What is Neha's current age?

Accepted Answer

Step 1: Let Neha's current age = x years. Then Meera's current age = 4x years. Step 2: After 8 years, Neha's age = x + 8 and Meera's age = 4x + 8. Step 3: Given that after 8 years, Meera's age = 2 × Neha's age, so 4x + 8 = 2(x + 8). Step 4: 4x + 8 = 2x + 16. Step 5: 2x = 8, therefore x = 4. Step 6: Neha's current age = 4 years.

Question 17

The present ages of Aman and Bina are in the ratio 3:2. Six years from now, the ratio of their ages will be 5:4. What is the difference between their current ages?

Accepted Answer

Step 1: Let Aman's current age = 3x and Bina's current age = 2x (from ratio 3:2). Step 2: After 6 years, Aman's age = 3x + 6 and Bina's age = 2x + 6. Step 3: Given that after 6 years the ratio is 5:4, so (3x + 6)/(2x + 6) = 5/4. Step 4: Cross-multiply: 4(3x + 6) = 5(2x + 6). Step 5: 12x + 24 = 10x + 30. Step 6: 12x - 10x = 30 - 24. Step 7: 2x = 6, so x = 3. Step 8: Aman's current age = 3(3) = 9 years, Bina's current age = 2(3) = 6 years. Step 9: Difference = 9 - 6 = 3 years.

Question 18

If A:B = 3:5 and B:C = 2:3, what is A:B:C?

Accepted Answer

Step 1: A:B = 3:5 means A = 3k, B = 5k for some constant k. Step 2: B:C = 2:3 means B = 2m, C = 3m for some constant m. Step 3: Since B is common, 5k = 2m, so m = 5k/2. Step 4: C = 3m = 3 × (5k/2) = 15k/2. Step 5: To avoid fractions, multiply all by 2: A:B:C = 6:10:15.

Question 19

Five years ago, the ratio of Priya's age to Deepak's age was 3:2. If Deepak is currently 30 years old, what is Priya's current age?

Accepted Answer

Step 1: Deepak's current age = 30 years. Step 2: Deepak's age 5 years ago = 30 - 5 = 25 years. Step 3: Ratio 5 years ago was Priya:Deepak = 3:2. Step 4: If Deepak's age 5 years ago = 25, then 25 corresponds to the '2' part of the ratio. Step 5: One ratio unit = 25 ÷ 2 = 12.5 years. Step 6: Priya's age 5 years ago = 3 × 12.5 = 37.5 years. Step 7: Priya's current age = 37.5 + 5 = 42.5 years.

Question 20

A shopkeeper mixes two types of tea costing ₹80 per kg and ₹120 per kg in the ratio 3:2. At what price per kg should he sell the mixture to gain 25% profit?

Accepted Answer

Step 1: Find the cost price of the mixture using alligation. In ratio 3:2, the mixture contains 3 parts of ₹80 tea and 2 parts of ₹120 tea. Step 2: Cost price of mixture = (3 × 80 + 2 × 120) / (3 + 2) = (240 + 240) / 5 = 480 / 5 = ₹96 per kg. Step 3: For 25% profit, selling price = 96 × 1.25 = ₹120 per kg. Therefore, the answer is ₹120 per kg.

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