Ratio and Proportion | Maths Olympiad Class 6 PDF Download

Q1: What was the initial volume of water in Bottle P if the ratio of water in Bottle P to Bottle Q is 3 : 4, and after Rajeev drank 40 mL from Bottle P, the ratio changed to 13 : 20?
(a) 60 mL
(b) 80 mL
(c) 300 mL
(d) 500 mL
Ans: (C)

• Let the initial volume of water in Bottle P be 3x and in Bottle Q be 4x.
• After Rajeev drinks 40 mL from Bottle P, the new ratio is 13 : 20.
• Setting up the equation: 20(3x - 40) = 4x × 13 leads to 60x - 800 = 52x.
• Solving gives 8x = 800, so x = 100.
• Thus, the initial volume in Bottle P is 3 × 100 = 300 mL.

Q2: If the price of a candy is 50 paise and the price of an ice cream is ₹ 20, what is the ratio of the price of a candy to the price of an ice cream?
(a) 40 : 1
(b) 1 : 40
(c) 1 : 20
(d) 1 : 10
Ans: B

• Cost of 1 candy is 50 paise.
• Cost of 1 ice cream is ₹ 20, which is equal to 2000 paise (since ₹ 1 = 100 paise).
• The required ratio of the cost of candy to ice cream is 50 : 2000.
• This simplifies to 1 : 40, meaning for every 1 candy, there are 40 ice creams in terms of cost.

Q3: A pole is divided into two segments in the ratio of 8 : 9. If the combined length is 1615 m, what is the length of the shorter segment?
(a) 420 m
(b) 670 m
(c) 760 m
(d) 1000 m
Ans: (C)

• Let the lengths of the two segments be represented as 8x and 9x.
• The total length can be expressed as 8x + 9x = 1615.
• This simplifies to 17x = 1615, leading to x = 95 m.
• Therefore, the length of the shorter segment is calculated as 8x = 8 × 95 = 760 m.

Q4: In a cricket training camp, there are 1200 children participating. Out of these, 900 are chosen for different matches. What is the ratio of the children who were not selected to the total number of children?
(a) 300 : 120
(b) 4 : 1
(c) 1 : 4
(d) 120 : 400
Ans: (C)

• Total number of children: 1200
• Number of selected children: 900
• Number of non-selected children: 1200 – 900 = 300
• Required ratio: 300 : 1200 simplifies to 1 : 4

Q5: In a quiz competition, the ratio of correct responses to incorrect responses is 5 : 2. If a participant provides 16 incorrect responses, how many correct responses did they give?
(a) 80
(b) 40
(c) 20
(d) 30
Ans: B

• Let the number of correct responses be represented as 5x and the number of incorrect responses as 2x.
• From the problem, we know that 2x = 16.
• To find x, we divide 16 by 2, which gives us x = 8.
• Now, to find the number of correct responses, we calculate 5x = 5 * 8 = 40.

Q6: The cost of a table and a chair is in the ratio of 7 : 5. If the table is priced ₹ 480 more than the chair, what is the price of the chair?
(a) ₹ 600
(b) ₹ 1000
(c) ₹ 1200
(d) ₹ 2000
Ans: (C)

• Let the price of the table be ₹ 7x and the price of the chair be ₹ 5x.
• From the problem, we know that 7x = 480 + 5x.
• By simplifying, we get 2x = 480, which leads to x = 240.
• Thus, the price of the chair is ₹ (5 × 240) = ₹ 1200.

Q7: A bag contains one rupee, 50 paise and 25 paise coins in the ratio 5 : 6 : 8. If the total amount is ₹ 420, then find the total number of coins.
(a) 798
(b) 789
(c) 978
(d) 987
Ans: (A)

• Let the number of ₹ 1 coins be 5x, the number of 50 paise coins be 6x, and the number of 25 paise coins be 8x.
• According to the problem, we can set up the equation: 5x × 100 + 6x × 50 + 8x × 25 = 420 × 100.
• This simplifies to: 500x + 300x + 200x = 42000.
• Combining the terms gives us 1000x = 42000, leading to x = 42.
• Calculating the number of coins: ₹ 1 coins = 5 × 42 = 210, 50 paise coins = 6 × 42 = 252, and 25 paise coins = 8 × 42 = 336.
• Finally, the total number of coins is 210 + 252 + 336 = 798.

Q8: Cost of 4 dozen bananas is ₹ 60. How many bananas can be bought for ₹ 22.50?
(a) 12
(b) 18
(c) 10
(d) 16
Ans: (B)

• Cost of 4 dozen bananas, which is 4 × 12 = 48 bananas, is ₹ 60.
• To find the cost of 1 banana, we calculate ₹ 60 divided by 48, which gives us ₹ 1.25 per banana.
• Now, to find out how many bananas can be bought for ₹ 22.50, we divide ₹ 22.50 by the cost of one banana (₹ 1.25).
• This results in 22.50 ÷ 1.25 = 18 bananas.

Q9: How is a profit of ₹ 3000 distributed among X, Y, and Z in the ratio of 2 : 3 : 1? What is the additional amount Y receives compared to X?
(a) ₹ 1000
(b) ₹ 1600
(c) ₹ 500
(d) ₹ 800
Ans: (C)

• Let the amounts received by X, Y, and Z be ₹ 2m, ₹ 3m, and ₹ m respectively.
• From the total profit, we have the equation: 2m + 3m + m = 3000.
• This simplifies to 6m = 3000, leading to m = 500.
• Thus, Y receives ₹ 3m = 3 × 500 = ₹ 1500, while X receives ₹ 2m = 2 × 500 = ₹ 1000.
• Therefore, Y gets ₹ (1500 – 1000) = ₹ 500 more than X.