Question

Ajay’s present age is 5 more than three times the age of Vijay . Shyam’s age is half the age of Ajay . If the ratio of the sum of Ajay and Vijay ‘s age to three times of Shyam’s age is 5:6 . Find Vijay’s age .

Answer 1

Answer:

let be age of Vijay is x

then age of ajay =3x + 5

and age of shayam = (3x + 5)/2

as the given info answer is 5 years

Vijay is 5 years old.

Answer 2

Answer:

• Vijay's age is 5 years.

Step-by-step explanation:

Given that:

• Ajay's present age is 5 more than three times the age of Vijay.
• Shyam's age is half the age of Ajay.
• Ratio of the sum of Ajay's and Vijay's age to three times of Shyam's age is 5 : 6.

To find:

• Vijay's age

Let us assume:

• Vijay's age be x.

Then,

• Ajay's age is (3x + 5)
• Shyam's age is (3x + 5) / 2.

Sum of Ajay's and Vijay's age:

= x + (3x + 5)

Opening the brackets,

= x + 3x +5

Adding x and 3x,

4x + 5

Three times Shyam's age:

= 3 × [(3x + 5)/2]

= 9x + 15/2

As it is given that, ratio of sum of Ajay's and Vijay's age to three times of Shyam’s age is 5:6.

Therefore,

$\sf{\dfrac{4x + 5}{\dfrac{9x + 15}{2}}= \dfrac{5}{6}}\\\\\longrightarrow \dfrac{(4x + 5)\times2}{9x + 15} = \dfrac{5}{6}\\\\\longrightarrow \dfrac{8x + 10}{9x + 15}=\dfrac{5}{6}$

By cross-multiplication,

$\longrightarrow \sf{6(8x+10)=5(9x+15)}$

Opening the brackets,

$\longrightarrow \sf{48x + 60=45x+75}$

Transposing variables and constants on different sides,

$\longrightarrow \sf{48x-45x=75-60}$

Subtracting 45x from 48x and 60 from 75,

$\longrightarrow\sf{3x=15}$

Transposing 3 from LHS to RHS and changing its sign,

$\longrightarrow \sf{x= \dfrac{15}{3}}$

Dividing 15 by 3,

$\longrightarrow \sf{x=5}$

Hence, x = 5

Therefore,

• Vijay's age = 5 years
• Ajay's age = (3 × 5) + 5 = 15 + 5 = 20 years
• Shyam's age = 20/2 = 10 years

Verification:

Sum of Vijay's and Ajay's age:

= (5 + 20) years

Adding 5 and 20,

= 25 years

Three times Shyam's age:

= (3 × 10) years

Multiplying 3 and 10,

= 30 years

Ratio of sum of Ajay's and Vijay's age to three times of Shyam’s age:

$\sf{= \dfrac{25}{30}}\\\\= \dfrac{25\div5}{30\div5}\\\\= \dfrac{5}{6}\\\\= 5 : 6$

Hence, Verified.