Question

Rohan's father is 5 years older than twice the Rohan's
age. His mother's age is the sum of his age and one
third of his father's age. His sister is 2 years younger to
him. The sum of their ages is 118 years,
Choose the correct option,
1. What is the age of Rohan (in years)?
b. 20
d. 45
2. What is the age of Rohan's sister in years)?
a 18
b. 20
c. 35
d. 45
3. What is the age of Rohan's mother (In years)?
18
15, 20
Rasmi
d. 45
4. What is the age of Rohan's father (in years)?
b. 20
d. 45​

Answer 1

Rohans age is 20

His father's age is 60

Sisters age is 18

Answer 2

Answer:

1. b

2. a

3. Rohans mothers age is 35 years( incomplete question)

4. d

Explanation:

Let us consider Rohan's age to be 'x' and his father's age to be 'y'.

Therefore, our equation is y=2x+5. ........(i)

Now, we will consider his mother's age to be z.

Therefore the equation is z=x+1/3y........(ii)

Let us consider the sister's age to be 'a'.

Theerefore the equation is a=x-2.....(iii)

it is also given that the sum of their ages is 118.

Therefore, x+y+z+a=118.........(iv)

now we will substitute the values of z and a in equation (iv)

x+y+x+1/3y+x-2=120

Solving the above

3x+ 4/3y= 116

let us also substitute the value for y in this equation

3x+4/3(2x+5) = 120

solving the above we get

3x+ 8/3x+ 20/3= 120

Multiplying the above equation by 3 we get,

9x+8x+20=360

solving,

17x=340

therefore x= 20.

substituting the value of x in equation (i) we get

y=2x+5. ........(i)

y= 2x20 + 5

y= 45

substituting the values of x and y in equation (ii) we get

z=x+1/3y........(ii)

z=20+1/3x15

z=20+15

z=35

substituting the value of x in equation (iv) we get

a=x-2

a=20-2

a=18

Therefore the agess of Rohan, his father, his mother and his sister are

20,45,35 and 18 respectively.