Question 1

Q1: Find the ratio of the following. (a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour. (b) 5 m to 10 km (c) 50 paise to ₹ 5

Accepted Answer

(a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour. Given: Speed of cycle = 15 km/hr Speed of scooter = 30 km/hr Solution: The units for both speeds are the same (km/hr), so we can find the ratio directly. Ratio = Speed of cycle : Speed of scooter $$= 15 : 30$$ To simplify, w...

Question 2

Q2: Convert the following ratios to percentages. (a) $3:4$ (b) $2:3$

Accepted Answer

(a) 3:4 Given: Ratio = $3:4$ Solution: The ratio $3:4$ can be written as the fraction $\frac{3}{4}$. To convert a fraction to a percentage, we multiply it by 100 and add the '%' symbol. Percentage = $\frac{3}{4} 	imes 100\%$ $$= 3 	imes 25\%$$ $$= 75\%$$ Final Answer: The percentage is $75\%$. (b)...

Question 3

Q3: $72\%$ of 25 students are interested in mathematics. How many are not interested in mathematics?

Accepted Answer

Given: Total number of students = 25 Percentage of students interested in mathematics = $72\%$ To Find: The number of students not interested in mathematics. Solution: First, we find the percentage of students who are not interested in mathematics. Percentage of students not interested = Total perce...

Question 4

Q4: A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in...

Accepted Answer

Given: Number of matches won = 10 Win percentage = $40\%$ To Find: The total number of matches played. Let: The total number of matches played be $x$. Solution: According to the problem, $40\%$ of the total matches played is equal to the number of matches won. So, we can write the equation: $$40\% \...

Question 5

Q5: If Chameli had ₹ 600 left after spending $75\%$ of her money, how much did she have in the beginning?

Accepted Answer

Given: Money left with Chameli = ₹ 600 Percentage of money spent = $75\%$ To Find: The total amount of money she had in the beginning. Let: The total money she had in the beginning be ₹ $x$. Solution: First, we find the percentage of money left. Percentage of money left = Total percentage - Percenta...

Question 6

Q6: If $60\%$ people in a city like cricket, $30\%$ like football and the remaining like other games, then what per cent of the people like other games? I...

Accepted Answer

Given: Percentage of people who like cricket = $60\%$ Percentage of people who like football = $30\%$ Total number of people = 50 lakh = 50,00,000 Part 1: Find the percentage of people who like other games. Solution: The total percentage of people is $100\%$. Percentage of people who like other game...

Question 7

Q1: During a sale, a shop offered a discount of $10\%$ on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked...

Accepted Answer

Given: Discount rate = $10\%$ Marked Price (MP) of a pair of jeans = ₹ 1450 Marked Price (MP) of one shirt = ₹ 850 To Find: Total amount the customer has to pay. Solution: Step 1: Calculate the sale price of the jeans. MP of jeans = ₹ 1450 Discount = $10\%$ of MP Discount amount = $10\% 	imes 1450...

Question 8

Q2: The price of a TV is ₹ 13,000. The sales tax charged on it is at the rate of $12\%$. Find the amount that Vinod will have to pay if he buys it.

Accepted Answer

Given: Price of the TV (selling price) = ₹ 13,000 Sales tax rate = $12\%$ To Find: The total amount Vinod will have to pay. Solution: Sales tax is calculated on the selling price of the item. Sales tax amount = $12\%$ of ₹ 13,000 $$= \frac{12}{100} 	imes 13000$$ $$= 12 	imes 130$$ $$= ₹ 1560$$ The...

Question 9

Q3: Arun bought a pair of skates at a sale where the discount given was $20\%$. If the amount he pays is ₹ 1,600, find the marked price.

Accepted Answer

Given: Discount rate = $20\%$ Amount paid (Sale Price, SP) = ₹ 1,600 To Find: The Marked Price (MP). Let: The Marked Price be ₹ $x$. Solution: The discount is always calculated on the Marked Price. Discount amount = $20\%$ of MP = $20\%$ of $x = \frac{20}{100}x = 0.2x$ Sale Price is calculated as: S...

Question 10

Q4: I purchased a hair-dryer for ₹ 5,400 including $8\%$ VAT. Find the price before VAT was added.

Accepted Answer

Given: Price including VAT = ₹ 5,400 VAT rate = $8\%$ To Find: The price before VAT was added (original price). Let: The original price be ₹ $x$. Solution: The price including VAT is the sum of the original price and the VAT amount. VAT amount = $8\%$ of the original price = $8\%$ of $x = \frac{8}{1...

Question 11

Q5: An article was purchased for ₹ 1239 including GST of $18\%$. Find the price of the article before GST was added?

Accepted Answer

Given: Price including GST = ₹ 1239 GST rate = $18\%$ To Find: The price of the article before GST was added (original price). Let: The original price be ₹ $x$. Solution: The price including GST is the sum of the original price and the GST amount. GST amount = $18\%$ of the original price = $18\%$ o...

Question 12

Q1: The population of a place increased to 54,000 in 2003 at a rate of $5\%$ per annum (i) find the population in 2001. (ii) what would be its population...

Accepted Answer

Given: Population in 2003 (A) = 54,000 Rate of increase (R) = $5\%$ per annum Formula for population growth: $$A = P \left(1 + \frac{R}{100}\right)^n$$ Where A is the final population, P is the initial population, R is the rate of growth, and n is the number of years. (i) Find the population in 2001...

Question 13

Q2: In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of $2.5\%$ per hour. Find the bacteria at the end of 2 hours...

Accepted Answer

Given: Initial count of bacteria (P) = 5,06,000 Rate of increase (R) = $2.5\%$ per hour Time (n) = 2 hours To Find: The count of bacteria at the end of 2 hours (A). Formula for growth: $$A = P \left(1 + \frac{R}{100}\right)^n$$ Solution: Substituting the given values into the formula: $$A = 506000 \...

Question 14

Q3: A scooter was bought at ₹ 42,000. Its value depreciated at the rate of $8\%$ per annum. Find its value after one year.

Accepted Answer

Given: Initial value of the scooter (P) = ₹ 42,000 Rate of depreciation (R) = $8\%$ per annum Time (n) = 1 year To Find: The value of the scooter after one year (V). Formula for depreciation: $$V = P \left(1 - \frac{R}{100}\right)^n$$ Where V is the final value, P is the initial value, R is the rate...

NCERT Solutions