Ratio, Proportion
- The ratio of ages of two students is 3 : 2. One is older to the other by 5 years. What is the age of the younger student ?
-
View Hint View Answer Discuss in Forum
Let their age be 3x and 2x years.
∴ 3x – 2x = 5
⇒ x = 5
∴ Younger student’s age
= 2x = 2 × 5 = 10 yearsCorrect Option: B
Let their age be 3x and 2x years.
∴ 3x – 2x = 5
⇒ x = 5
∴ Younger student’s age
= 2x = 2 × 5 = 10 years
- In an ornament the ratio of gold and copper is 3 : 2. The percentage of gold in the ornament is :
-
View Hint View Answer Discuss in Forum
Gold : Copper = 3 : 2
Sum of the terms of ratio
= 3 + 2 = 5∴ Percentage of gold = 3 × 100 5
= 60%Correct Option: A
Gold : Copper = 3 : 2
Sum of the terms of ratio
= 3 + 2 = 5∴ Percentage of gold = 3 × 100 5
= 60%
- The ratio of the number of boys and girls in a school is 8 : 12. If 50% of boys and 25% of girls are getting scholarships for their studies, what is the percentage of school students who are not getting any scholarships ?
-
View Hint View Answer Discuss in Forum
Number of boys = 8x
Number of girls = 12x
Students who do not get scholarships :
Boys ⇒ 4xGirls ⇒ 12x × 75 = 9x 100
Their sum = 4x + 9x = 13x∴ Required percent = 13x × 100 20x
= 65%Correct Option: A
Number of boys = 8x
Number of girls = 12x
Students who do not get scholarships :
Boys ⇒ 4xGirls ⇒ 12x × 75 = 9x 100
Their sum = 4x + 9x = 13x∴ Required percent = 13x × 100 20x
= 65%
- 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 :
-
View Hint View Answer Discuss in Forum
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
-
View Hint View Answer Discuss in Forum
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
