Question

The ages of Radha and meera are in the ratio 5:7. four years from now the ratio of their ages will be 3:4 find their present age
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Answer 1

Given :

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

To Find :

• Present Ages of Radha and Meera .

Solution :

$\longmapsto\tt{Let\:Present\:Age\:of\:Radha=5x}$

$\longmapsto\tt{Let\:Present\:Age\:of\:Meera=7x}$

After 4 years :

$\longmapsto\tt{Age\:of\:Radha=5x+4}$

$\longmapsto\tt{Age\:of\:Meera=7x+4}$

A.T.Q :

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

$\longmapsto\tt{4(5x+4)=3(7x+4)}$

$\longmapsto\tt{20x+16=21x+12}$

$\longmapsto\tt{20x-21x=12-16}$

$\longmapsto\tt{-x=-4}$

$\longmapsto\tt\bf{x=4}$

Value of x is 4 .

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Radha=5(4)}$

$\longmapsto\tt\bf{20\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:Meera=7(4)}$

$\longmapsto\tt\bf{28\:yrs}$

Answer 2

Given information,

The ages of Radha and Meera are in the ratio 5:7. four years from now the ratio of their ages will be 3:4. Find their present ages.

• Ratio of Radha and Meera age = 5:7
• Four years from now ratio of their ages = 3:4

Let,

• Their present ages = 5y years and 7y years

Their ages four years from now,

• Age of Radha = (5y + 4) years
• Age of Meera = (7y + 4) years

According to the Question,

• Four years from now ratio of their ages = 3:4

Therefore,

➻ (5y + 4)/(7y + 4) = 3/4

By cross multiplication,

➻ 4(5y + 4) = 3(7y + 4)

➻ 20y + 16 = 21y + 12

➻ 20y - 21y = 12 - 16

➻ -1y = -4

➻ 1y = 4

➻ y = 4

Now,

◕ Present age of Radha = 5y

◕ Present age of Radha = 5 × 4

◕ Present age of Radha = 20 years

Also,

◕ Present age of Meera = 7y

◕ Present age of Meera = 7 × 4

◕ Present age of Meera = 28 years

Verification,

• Four years from now ratio of their ages = 3:4

Therefore,

➻ (5y + 4)/(7y + 4) = 3/4

Putting value of y,

➻ (5 × 4 + 4)/(7 × 4 + 4) = 3/4

➻ (20 + 4)/(28 + 4) = 3/4

➻ 24/32 = 3/4

➻ 3/2 = 3/2

➻ LHS = RHS

Hence, Verified ✔

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