Question

Solve the following problem
. The ages of Ramu and Somu are in the ratio 5:7 four years from now the ratio of
their ages will be 3:4. Find their present ages.
​

Answer 1

Answer :-

• Ramu's age is 20 years.
• Somu's age is 28 years.

Given :-

• The ages of Ranu and Somu are in the ratio 5 : 7.
• Four years from now, the ratio of their ages will be 3 : 4.

To find :-

• Their present ages.

Step-by-step explanation :-

• The ages of Ramu and Somu are in the ratio 5 : 7, so let their ages be 5x and 7x respectively.

After four years,

• Ramu's age will be 5x + 4.
• Somu's age will be 7x + 4.

It has been given that :-

• After four years, the ages of Ramu and Somu will be in the ratio 3 : 4.

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$\sf\dfrac{5x + 4}{7x + 4} = \dfrac{3}{4}$

By cross multiplication,

$\sf4 \: (5x + 4) = 3 \: (7x + 4)$

Removing the brackets,

$\sf20x + 16 = 21x + 12$

Putting the constant and variable terms on different sides by the method of transposition,

$\sf20x - 21x = 12 - 16$

On simplifying,

$\sf \cancel{-} x = \cancel{-} 4$

Cutting off the negative sign,

$\underline{ \boxed{\sf x = 4}}$

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Hence, their present ages are :-

$\rm Ramu's \: age = 5x = 5 \times 4 = 20.$

$\rm Somu's \: age = 7x = 7 \times 4 = 28.$

Answer 2

Answer:

The Present Age of Ramu is 20 years

The Present Age of Somu is 28 years

Step-by-step explanation:

Given,

• The Ratio of Present Ages of Ramu and Somu is 5 : 7.

After 4 years,

• The Ratio of Their Ages becom 3 : 4.

To Find,

• The Present Ages of Ramu and Somu.

Solution,

Let's,

The Present Age of Ramu = 5X

So,

The Present Age of Somu = 7X

After 4 years,

The Age of Ramu = 5X + 4

The Age of Somu = 7X + 4

The Ratio of Their Ages After 4 years = 3 : 4

→ (5X + 4) : (7X + 4) = 3 : 4

→ (5X + 4)/(7X + 4) = 3/4

→ 4(5X + 4) = 3(7X + 4)

→ 4(5X) + 4(4) = 3(7X) + 3(4)

→ 20X + 16 = 21X + 12

→ 16 - 12 = X

→ X = 4

The Present Age of Ramu = 5X

→ The Present Age of Ramu = 5(4)

The Present Age of Ramu = 20 years

The Present Age of Somu = 7X

→ The Present Age of Somu = 7(4)

The Present Age of Somu = 28 years

Required Answer,

The Present Age of Ramu = 20 years

The Present Age of Somu = 28 years