Proportional Reasoning 1 Class 8 Short Question Answer

Proportional Reasoning 1 Class 8 Short Question Answer

Proportional Reasoning 1 Class 8 Short Question Answer

Question 1.

Find two numbers whose sum is 100 and who are in the ratio 9 : 16.

Solution:

Let the numbers be 9x and 16x.

So, 9x + 16x = 100

or 25x = 100 or x = [latex]\frac{100}{25}[/latex] = 4.

So, the numbers are 9 × 4 and 16 × 4, i.e., 36 and 64.

Question 2.

In an election, the votes cast for two of the candidates were in the ratio 5 : 7. If the successful candidate received 20734 votes, how many votes did his opponent receive?

Solution:

Ratio of votes is 5 : 7.

The successful candidate has received 20734 votes. Let votes received by the opponent hex..

Therefore, x : 20734 : : 5 : 7

(Because opponent has received less votes)

So, x × 7 = 20734 × 5

or x = [latex]\frac{20734 \times 5}{7}[/latex] = 2962 × 5

= 14810.

Question 3.

A recipe for raspberry jelly calls for 5 cups of raspberry juice and 2[latex]\frac{1}{2}[/latex] cups of sugar. Find the amount of sugar needed for 6 cups of the juice?

Solution:

Let in 6 cups of juice, sugar be x cups. It is given that for 5 cups of juice, sugar is 2[latex]\frac{1}{2}[/latex] cups or [latex]\frac{5}{2}[/latex]cups.

So, we have : 6 : 5 : : x : [latex]\frac{5}{2}[/latex]

or 6 x [latex]\frac{5}{2}[/latex] = 5 × x

or x = [latex]\frac{6 \times 5}{2 \times 5}[/latex] = 3 cups

Question 4.

A farmer planted 1890 tomato plants in a field in rows each having 63 plants. A certain type of worm destroyed 18 plants in each row. How many plants did the worm destroy in the whole field?

Solution:

Number of rows = 1890 ÷ 63 = 30.

In one row, plants destroyed by worms = 18

So, in 30 rows, number of plants destroyed = 18 × 30 = 540.

Question 5.

Length and breadth of the floor of a room are 5 m and 3 m, respectively. Forty tiles, each with area [latex]\frac{1}{16}[/latex]m² are used to cover the floor partially. Find the ratio of the tiled and the non-tiled portions of the floor.

Solution:

Area of the room

= 5 × 3 = 15 m².

Area of the tiled portion

= 40 × [latex]\frac{1}{16}[/latex] m² = [latex]\frac{5}{2}[/latex]m²

So, area of the untiled portion

= (15 - [latex]\frac{5}{2}[/latex])m² = [latex]\frac{25}{2}[/latex]m²

So, required ratio

= [latex]\frac{5}{2}[/latex] : [latex]\frac{25}{2}[/latex] = 1 : 5

Question 6.

A carpenter had a board which measured 3m × 2m. She cut out a rectangular piece of 250 cm × 90 cm. What is the ratio of the area of cut out piece and the remaining piece?

Solution:

Area of the board

= 3 × 2 = 6 m²

= 6 × 100 × 100 cm²

= 60000 cm².

Area of the cut out rectangular piece

= 250 cm × 90 cm

= 22500 cm²

So, area of the remaining piece

= (60000 - 22500) cm²

= 37500 cm²

Thus, required ratio

= 22500 : 37500 = 3 : 5.