Comparing Quantities-NCERT Solutions

          In a primary school, the parents were asked about the cumber of hours they spend per day in helping their children to o homework. There were 90 parents who helped for hour to 1 hours. The distribution of parents according to the time for which, they said they helped is given in the adjoining figure; 20% helped for more than 1 hours per day; 30% helped for hour to 1 hours; 50% did not help at all.

          Using this, answer the following:

          (i) How many parents were surveyed?

          (ii) How many said that they did not help?

          (iii) How many said that they helped for more than 1 - hours?

          (i) Since, 30% of total surveyed parents helped their children hours”. And 90 parents helped their children for “ hours to 1 hours”.

              ∴ 30% [surveyed parents] = 90

              

          (ii) Since 50% of the surveyed parents did not help their children.

              ∴ Number of parents who did not help = 50% of of surveyed parents

              = 50% of 300

              

          (iii) Since 20% of the surveyed parents help their children for more than 1 hours. i.e. 20% of surveyed parents help for more than 1 hours.

              ∴ Number of parents helped for more than 1 hours = 20% of 300

              

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 poise to Rs 5

          In a ratio, the quantities are in the same unit If they are not in the same units, then first we convert them in the same unit.

          (a) Speed of cycle = 15 km per hour

              Speed of scooter = 30 km per hour

          

Question 2. Convert the following ratios to percentages.

              (a) 3 : 4                            (b) 2 : 3

Solution:

                

              72% of 25 students are good in Mathematics. How many are not good in Mathematics?

              ∴ 72% of 25 are good in Mathematics.

              ∴ (100 - 72)% of 25 students are not good in Mathematics.

              or 28% of 25 students are not good in Mathematics

              or students are not good in Mathematics.

              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?

              Number of matches won by the team = 10

              The team won 40% of total number of match.

              40% of [Total number of match] = 10

              or [Total number of match] = 10

              or Total number of matches

              Thus, the total number of match played = 25

              If Chameli had Rs 600 left after spending 75% of her money, how much did she in the beginning?

              Chameli made spending of Rs 75%.

              She is left with Rs (100 75)% or Rs 25%.

              But she is having Rs 600 now.

              25% of total money = Rs 600

              or of total money = Rs 600

              or Total money

              Thus, she had Rs 2400 in the beginning.

              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.

              People who like cricket = 60%

              People who like football = 30%

              People who like other games = [100 - (60 + 30)]% _ [100 90]%

              = [100 – 90]% = 10%

              Now, Total number of people = 50,00,000

              

              Thus, number of people who like

              Cricket = 30,00,000

              Football = 15,00,000

              Other games = 5,00,000