Chapter 8 Comparing Quantities Exercise 8.1
Question 1: 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 Rs 5
Answer:
(a)
Speed of cycle = 15 km per hour
Speed of scooter = 30 km per hour
Ratio = speed of cycle/speed of scooter
= 15/30
= 1/2
= 1 : 2
(b)
Number of meter = 5 m
Number of kilometer = 10 km
Ratio = number of m/number of km
= 5/10000 [Since, 1 km = 1000 m, 10 km = 10000 m (10 × 1000 = 10000)]
= 1/2000
= 1 : 2000
(c)
Number of paise = 50 paise
Number of rupees = ₹5
Ratio = number of paise/number of rupees
= 50/500 [Since, ₹1 = 100 paise, ₹5 = 500 paise (5 × 100 = 500)]
= 1/10
= 1 : 10
Question 2: Convert the following ratios to percentages.
(a) 3 : 4
(b) 2 : 3
Answer:
(a)
= 3 : 4 = 3/4
= 3/4 × 100
= 300/4
= 75%
(b)
= 2 : 3 = 2/3
= 2/3 × 100
= 200/3
= 66.66%
Question 3: 72% of 25 students are good in mathematics. How many are not good in mathematics?
Answer:
Total number of students = 25
Percentage of students who are good in mathematics = 72%
= 72/100 × 25
= 1800/100
= 18
Number of students who are not good in mathematics = ?
= Total number of students - Number of students who are good in mathematics
= 25 - 18
= 7
Therefore, 7 students are not good in mathematics.
Question 4: 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 all?
Answer:
Number of matches who by football team = 10
Win percentage = 40%
Matches played by the team = ?
Let the total number of matches played by the football team be x.
= 40/100 × x = 10
= 2x/5 = 10
= 2x = 10 × 5
= 2x = 50
= x = 50/2
= x = 25
Therefore, the total number of matches played by the football team was 25.
Question 5: If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning?
Answer:
Amount left with Chameli = ₹600
Percentage of spent money = 75%
Money Chameli had in the beginning = ?
Let the money that Chameli had in the beginning be x.
= 75/100 × x = 600
= x/4 = 600
= x = 600 × 4
= x = ₹2400
Therefore, the total money Chameli had in the beginning was ₹2400.
Question 6: 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? If the total number of people are 50 lakh, find the exact number who like each type of game.
Answer:
Total number of people in the city = 5000000
Percentage of people who like cricket = 60%
Percentage of people who like football = 30%
Percentage of people who like other games = ?
= 100 - (Percentage of people who like cricket + Percentage of people who like football)
= 100 - (60 + 30)
= 100 - 90
= 10%
Therefore, 10% of the people like other games.
Total number of people in the city = 5000000
Percentage of people liking cricket = 60%
= 60/100 × 5000000
= 60 × 5000000/100
= 300000000/100
= 3000000/1
Therefore, 3000000 people in the city like cricket.
Total number of people in the city = 5000000
Percentage of people liking football = 30%
= 30/100 × 5000000
= 30 × 5000000/100
= 150000000/100
= 1500000/1
Therefore, 1500000 people in the city like football.
Total number of people in the city = 5000000
Percentage of people liking other games = 10%
= 10/100 × 5000000
= 10 × 5000000/100
= 50000000/100
= 500000/1
Therefore, 500000 people in the city like other games.
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