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

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- Time and Work
- Time and Distance
- Ratio and Proportion
- Average
- Percentage
- Profit and Loss
- Hour Clock Arithmetic
- Day Arithmetic
- Month Arithmetic
- Equations
- Odd man out
- Problems on Ages
- Pipes and Cisterns
- Boats and Streams
- Mixture Problems
- Problems on Trains