Ratio, Proportion
- A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black socks is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was :
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Number of brown socks = x
Price of brown socks = ₹ y per pair
Price of black socks = ₹ 2y per pair
∴ 4y + x × 2y= 150 (4 × 2y + xy) 100 ⇒ 4 + 2x = 3 (8 + x) 2
⇒ 8 + 4x = 24 + 3x
⇒ x = 24 – 8 = 16
∴ Required ratio = 4 : 16
= 1 : 4Correct Option: B
Number of brown socks = x
Price of brown socks = ₹ y per pair
Price of black socks = ₹ 2y per pair
∴ 4y + x × 2y= 150 (4 × 2y + xy) 100 ⇒ 4 + 2x = 3 (8 + x) 2
⇒ 8 + 4x = 24 + 3x
⇒ x = 24 – 8 = 16
∴ Required ratio = 4 : 16
= 1 : 4
- A milkman makes 20% profit by selling milk mixed with water at 9 per litre. If the cost price of 1 litre pure milk is 10, then the ratio of milk and water in the mixture is
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Milk : Water = K : 1
∴ S.P. = (K + 1) × 9
C.P. = 10K
Gain = 9 – KGain % = 9 − K × 100 10K ⇒ 9 − K × 100 = 20 10K
⇒ 90 – 10K = 20K
⇒ 30K = 90 ⇒ K = 3
∴ Ratio = 3 : 1Correct Option: A
Milk : Water = K : 1
∴ S.P. = (K + 1) × 9
C.P. = 10K
Gain = 9 – KGain % = 9 − K × 100 10K ⇒ 9 − K × 100 = 20 10K
⇒ 90 – 10K = 20K
⇒ 30K = 90 ⇒ K = 3
∴ Ratio = 3 : 1
- There is a ratio of 5 : 4 between two numbers. If 40 per cent of the first is 12, then 50% of the
second number is
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Let numbers = 5x and 4x
∴ 5x × 40 = 12 100
⇒ 2x = 12 ⇒ x = 6 and
Second number = 6 × 4 = 24∴ 50% of 24 = 24 × 50 = 12 100 Correct Option: A
Let numbers = 5x and 4x
∴ 5x × 40 = 12 100
⇒ 2x = 12 ⇒ x = 6 and
Second number = 6 × 4 = 24∴ 50% of 24 = 24 × 50 = 12 100
- The reciprocals of the squares of the numbers
1 1 and 1 1 . are in the ratio 2 3
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Ratio of the squares of 3 and 4 2 3 = 9 : 16 4 9
Ratio of their reciprocals= 4 : 9 9 16
= 64 : 81Correct Option: A
Ratio of the squares of 3 and 4 2 3 = 9 : 16 4 9
Ratio of their reciprocals= 4 : 9 9 16
= 64 : 81
- Rs. 782 is divided into three parts in the ratio
1 : 2 : 3 , the first part is 2 3 4
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A : B : C = 1 : 2 : 3 2 3 4 = 1 × 12 : 2 × 12 : 3 × 12 2 3 4
= 6 : 8 : 9
Sum of the terms of ratio
= 6 + 8 + 9 = 23
∴ First part= Rs. 6 × 782 = Rs. 204 23 Correct Option: B
A : B : C = 1 : 2 : 3 2 3 4 = 1 × 12 : 2 × 12 : 3 × 12 2 3 4
= 6 : 8 : 9
Sum of the terms of ratio
= 6 + 8 + 9 = 23
∴ First part= Rs. 6 × 782 = Rs. 204 23