Ratio and Proportion Solution13

In this page ratio and proportion solution13 we are going to see solution of each question from the worksheet ratio and proportion.

(25)Two numbers are in the ratio 2 : 3 and the sum of their squares is 208. Find the numbers.

Solution:

Let “x” and “y” are the two numbers

x : y = 2 : 3

x/y =2/3

x = 2y/3

x² + y² = 208

(2y/3)² + y² = 208

(4y²/9) + y² = 208

(4 y² + 9 y²)/9 = 208

13 y² = 208 (9)

13 y² = 1872

y² = 1872/13

y² = 144

y =   √12 x 12

y = 12

(26) Two numbers are in the ratio 3 : 4 and their differences of their cubes is 999. Find the numbers.

Solution:

Let “x” and “y” are the two numbers

x : y = 3 : 4

x/y =3/4

x = 3y/4

x³ - y³ = 999

(3y/4)³ - y³ = 999

(27 y³/64)  - y³ = 999

(27y³ -64 y³)/64 = 999

-37 y³/64 = 999

- 37y³ = 999(64)

- 37y³ = 63936

y³ = 63936/(-37)

y³ = -1728

y = - (4 x 4 x 4 x 3 x 3 x 3)^1/3

y =4 (3)

y = -12

now we are going to substitute the value of y in the equation x = 3y/4

x =3(-12)/4

x = -9

Therefore the required two numbers are -9 and -12

(27) The ages of two men are in the ratio 3 : 4. In 10 years their ages will be in the ratio 5 : 6. Find their ages.

Solution:

Let 3 x ,4 x are the two ages of men

their ages are in the ratio 3 : 4

In 10 years their ages will be in the ratio 5 : 6.

(3 x + 10) : (4x + 10) = 5 : 6

(3x + 10)/(4x + 10) = 5/6

6(3 x + 10) = 5 (4 x + 10)

18 + 60 = 20 x + 50

18 – 20 x = 50 – 60

-2 x = -10

x = 10/2

x = 5

Therefore their ages = 3 (5) = 15 years

= 4 (5) = 20 years

ratio and proportion solution13 ratio and proportion solution13