Question

the present age of Shyam and Radha are in ratio 4:5. Ten years ago , their ages were in the ratio 3:4. What are their present ages​

Answer 1

Given :

• Present Ages of Shyam and Radha are in the ratio 4:5 .
• Ten years ago , their ages were in the ratio 3:4 .

To Find :

• Present Age of Shyam and Radha .

Solution :

$\longmapsto\tt{Let\:Present\:age\:of\:Shyam\:be=4x}$

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

Now ,

• Ten years ago , their ages were in the ratio 3:4 .

$\longmapsto\tt{Age\:of\:Shyam=4x-10}$

$\longmapsto\tt{Age\:of\:Radha=5x-10}$

A.T.Q :

$\longmapsto\tt{\dfrac{4x-10}{5x-10}=\dfrac{3}{4}}$

$\longmapsto\tt{4(4x-10)=3(5x-10)}$

$\longmapsto\tt{16x-40=15x-30}$

$\longmapsto\tt{16x-15x=-30+40}$

$\longmapsto\tt\bf{x=10}$

Value of x is 10 .

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Shyam=4(10)}$

$\longmapsto\tt\bf{40\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:Radha=5(10)}$

$\longmapsto\tt\bf{50\:yrs}$

Answer 2

Answer:

Given :-

$\leadsto$ The present age of Shyam and Radha are in the ratio of 4:5. Ten years ago, their ages were in the ratio of 3:4.

To Find :-

$\leadsto$ What are their present ages.

Solution :-

Let, the present age of Shyam be 4x

And, the present age of Radha will be 5x

$\mapsto$ After 10 years,

Age of Shyam be 4x - 10

And, the age of Radha will be 5x - 10

According to the question,

⇒ $\sf\dfrac{4x - 10}{5x - 10} =\: \dfrac{3}{4}$

By doing cross multiplication we get,

⇒ 4(4x - 10) = 3(5x - 10)

⇒ 16x - 40 = 15x - 30

⇒ 16x - 15x = - 30 + 40

➠ x = 10

Hence, their required present ages are,

✧ Present age of Shyam = 4x = 4 × 10 = 40 years

✧ Present age of Radha = 5x = 5 × 10 = 50 years

$\therefore$ The present age of Shyam is 40 years and the present age of Radha is 50 years .

$\boxed{\bold{\large{\star{VERIFICATION :-}}}}$

↦ $\sf\dfrac{4x - 10}{5x - 10} =\: \dfrac{3}{4}$

By doing cross multiplication we get,

↦ 4(4x - 10) = 3(5x - 10)

↦ 16x - 40 = 15x - 30

Put x = 10 we get,

↦ 16(10) - 40 = 15(10) - 30

↦ 160 - 40 = 150 - 30

↦ 120 = 120

➦ LHS = RHS

Hence, Verified ✔