# Comparing Quantities

## In Text Questions

**Example 1:** Find the percentage of children of different heights for the following data.

**Answer:**

Height | Number of children | In fraction | In percent |
---|---|---|---|

110 cm | 22 | 11/50 | 22% |

120 cm | 25 | 1/4 | 25% |

128 cm | 32 | 8/25 | 32% |

130 cm | 21 | 21/100 | 21% |

TOTAL | 100 | 1 | 100% |

**Example 2:** A shop has the following number of shoe pairs of different sizes. (Size 2: 20, Size 3: 30, Size 4: 28, Size5: 14, Size 6: 8) Write this information in tabular form as done earlier and find the percentage of each shoe size available in the shop.

**Answer:**

Size of shoes | No. of shoes | Percentage |
---|---|---|

2 | 20 | 20% |

3 | 30 | 30% |

4 | 28 | 28% |

5 | 14 | 14% |

6 | 8 | 8% |

TOTAL | 100 | 100% |

**Example 3:** A collection of 10 chips with different colours is given. Fill the table and find the percentage of chips of each colour.

**Answer:**

Colour | Number | Fraction | Percentage |
---|---|---|---|

Green | 4 | 2/5 | 40% |

Blue | 3 | 3/10 | 30% |

Red | 3 | 3/10 | 30% |

Total | 100 | 1 | 100% |

**Example 4:** Mala has a collection of bangles. She has 20 gold bangles and 10 silver bangles. What is the percentage of bangles of each type? Can you put it in the tabular form as done in the above examples?

**Answer:** Total number of bangles `= 20 + 10 = 30`

Percentage of gold bangles: `(20)/(30)xx100=66\2/3%`

Percentage of silver bangles: `(10)/(30)xx100=33\1/3%`

**Example 5:** What per cent of these figures are shaded?

**Answer:** (i) 3 out of four parts are shaded. Percentage of shaded parts can be calculated as follows: `3/4xx100=75%`

(ii) Total of shaded parts:

`=1/4+1/8+1/8`

`=(2+1+1)/(8)=4/8=1/2`

Percentage of shaded parts can be calculated as follows: `1/2xx100=50%`

**Example 6:** Find

(a) 50% of 164

**Answer:** `164xx(50)/(100)=82`

(b) 75% of 12

**Answer:** `12xx(75)/(100)=9`

(c) `12(1)/(2)`% of 64

**Answer:** `64xx12\1/2%`

`=64xx(25)/(2)xx(1)/(100)=8`

**Example 7:** 8% of children of a class of 25 like getting wet in the rain. How many children like getting wet in the rain?

**Answer:** `25xx(8)/(100)=2`

**Example 8:** Divide 15 sweets between Manu and Sonu so that they get 20% and 80% respectively.

**Answer:** Manu’s share: `15xx(20)/(100)=3`

Sonu's share: `15xx(80)/(100)=12`

**Example 9:** If angles of a triangle are in the ratio 2:3:4, find the value of each angle.

**Answer:** Since angle sum of a triangle is 180°. Hence, this can be calculated as follows:

`2x + 3x + 4x = 180°`

Or, `9x = 180°`

Or, `x = 180° ÷9 = 20°`

Hence, `2x = 20 xx 2 = 40°`

`3x = 20 xx 3 = 60°`

`4x = 20 xx 4 = 80°`

Hence, the angles are; 40°, 60° and 80°

**Example 10:** Find percentage of increase or decrease:

(a) Price of shirt decreased from Rs. 80 to Rs. 60.

**Answer:** Initial prices = Rs. 80 and final price = Rs. 60

Decrease in price `= 80 – 60 = Rs. 20`

Percentage decrease: `(20xx100)/(80)=25%`

(b) Marks in a test increased from 20 to 30.

**Answer:** Initial marks = 20 and final marks = 30

Increase in marks `= 30 – 20 = 10`

Percentage increase in marks: `(10xx100)/(20)=50%`

**Example 11:** My mother says, in her childhood petrol was Re. 1 a litre. It is Rs. 52 per litre today. By what percentage has the price gone up?

**Answer:** Initial price = Re. 1 and final price = Rs. 52

Increase in price `= 52 – 1 = Rs. 51`

Percentage increase in price:

`(51xx100)/(1)=5100%`

**Example 12:** A shopkeeper bought a chair for Rs. 375 and sold it for Rs. 400. Find the gain percentage.

**Answer:** CP = Rs. 375 and SP = Rs. 400

Profit `= SP – CP = 400 – 375 = Rs. 25`

Percentage profit:

`(text(Profit)xx100)/(CP)`

`=(25xx100)/(375)=(20)/(3)=6\2/3%`

**Example 13:** Cost of an item is Rs. 50. It was sold with a profit of 12%. Find the selling price.

**Answer:** CP = Rs. 50 and Profit = 12%

Profit: CP `xx` Percentage profit

`=50xx(12)/(100)=Rs. 6`

SP = CP + Profit `= 50 + 6 = Rs. 56`

**Example 14:** An article was sold for Rs. 250 with a profit of 5%. What was its cost price?

**Answer:** SP = Rs. 250 and profit = 5%

`CP=(SP\xx100)/(100+%text(Profit))`

`=(250xx100)/(105)=(5000)/(21)`

`=238(2)/(21)`

**Example 15:** An item was sold for Rs. 540 at a loss of 5%. What was its cost price?

**Answer:** SP = Rs. 540 and loss = 5%

`CP=(SPxx100)/(100-%text(Loss)`

`=(540xx100)/(95)=(10800)/(19)`

`=568(8)/(19)`

**Example 16:** You have Rs. 2,400 in your account and the interest rate is 5%. After how many years would you earn Rs. 240 as interest?

**Answer:** P = Rs. 2400, r = 5%, SI = Rs. 240 t = ?

`t=(SI\xx100)/(P\xx\r)`

`=(240xx100)/(2400xx5)=2` years

**Question 17:** On a certain sum the interest paid after 3 years is Rs. 450 at 5% rate of interest per annum. Find the sum.

**Answer:** SI = Rs 450, r = 5%, t = 3 years and P =?

`P=(SI\xx100)/(r\xx\t)`

`=(450xx100)/(5xx3)=Rs. 3000`