Top 5 questions related to Ratio for class 8.

1.If the ratio of chocolates to ice-cream cones in a box is 5:8 and the number of chocolates is 30, find the number of ice-cream cones.

Solution:

Let the number of chocolates be 5x and the number of ice-cream cones be 8x.

5x = 30 

→ x = 6.

Therefore, number of ice-cream cones in the box = 8*6 = 48.

2.Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers.

Solution:

Sum of the terms of the ratio = 3 + 4 = 7

Sum of numbers = 63

Therefore, first number = 3/7 × 63 = 27

Second number = 4/7 × 63 = 36

Therefore, the two numbers are 27 and 36.

3. If x : y = 1 : 2, find the value of (2x + 3y) : (x + 4y)

Solution:

x : y = 1 : 2 means x/y = 1/2

Now, (2x + 3y) : (x + 4y) = (2x + 3y)/(x + 4y) [Divide numerator and denominator by y.]

= [(2x + 3y)/y]/[(x + 4y)/2] = [2(x/y) + 3]/[(x/y) + 4], put x/y = 1/2

We get = [2 (1/2) + 3)/(1/2 + 4) = (1 + 3)/[(1 + 8)/2] = 4/(9/2) = 4/1 × 2/9 = 8/9

Therefore the value of (2x + 3y) : (x + 4y) = 8 :9.

4. A bag contains $510 in the form of 50 p, 25 p and 20 p coins in the ratio 2 : 3 : 4. Find the number of coins of each type. 

Solution: 

Let the number of 50 p, 25 p and 20 p coins be 2x, 3x and 4x. 

Then 2x × 50/100 + 3x × 25/100 + 4x × 20/100 = 510

x/1 + 3x/4 + 4x/5 = 510

(20x + 15x + 16x)/20 = 510 

⇒ 51x/20 = 510

x = (510 × 20)/51 

x = 200

2x = 2 × 200 = 400 

3x = 3 × 200 = 600 

4x = 4 × 200 = 800. 

Therefore, number of 50 p coins, 25 p coins and 20 p coins are 400, 600, 800 respectively. 

5.Set up all possible proportions from the numbers 8, 12, 20, 30.

Solution:

We note that 8 × 30 = 240 and 12 × 20 = 240

Thus, 8 × 30 = 12 × 20       ………..(I)

Hence, 8 : 12 = 20 : 30       ……….. (i)

We also note that, 8 × 30 = 20 × 12

Hence, 8 : 20 = 12 : 30       ……….. (ii)

(I) can also be written as 12 × 20 = 8 × 30

Hence, 12 : 8 = 30 : 20       ……….. (iii)

Last (I) can also be written as

12 : 30 = 8 : 20       ……….. (iv)

Thus, the required proportions are 8 : 12 = 20 : 30

8 : 20 = 12 : 30     12 : 8 = 30 : 20     12 : 30 = 8 : 20