Arun will be half as old as Lilly in 3 years. Arun will also be one-third as old as James in 5 years. If James is 15 years older than Lilly, how old is Arun?a)6b)8c)9d)5e)4Correct answer is option 'B'. Can you explain this answer?

Question

Answer

let age of Arun =x, Lilly =y James = z
(x+3) =1/2 *(y+3) so we have 2x-y =-3 -(1)
(x+5) =1/3 * (z+5) ; ⇒ 3x-z=-10 -(2)
From (1)&(2) we get, x+y-z =-7 -(3)
we have z =15+y – (4)
from equation 3 and 4 we get x=8

Answer

Answer

Let's break down the information given in the question:

- In 3 years, Arun will be half as old as Lilly.
- In 5 years, Arun will be one-third as old as James.
- James is 15 years older than Lilly.

We need to determine Arun's current age.

Let's assume Arun's current age is A, Lilly's current age is L, and James' current age is J.

From the given information, we can write the following equations:

1) In 3 years, Arun will be half as old as Lilly:
A + 3 = (L + 3)/2

2) In 5 years, Arun will be one-third as old as James:
A + 5 = (J + 5)/3

3) James is 15 years older than Lilly:
J = L + 15

Now, let's solve these equations to find the values of A, L, and J.

Solving equation 3 for L, we get:
L = J - 15

Substituting this value of L in equations 1 and 2, we get:
A + 3 = ((J - 15) + 3)/2
A + 5 = (J + 5)/3

Simplifying these equations, we have:
2A + 6 = J - 12 + 3
3A + 15 = J + 5

Rearranging the equations, we get:
2A - J = -15
3A - J = -10

Now, let's solve these two equations simultaneously to find the values of A and J.

Multiplying the first equation by 3 and the second equation by 2, we get:
6A - 3J = -45
6A - 2J = -20

Subtracting these two equations, we eliminate A:
-3J + 2J = -45 - (-20)
-J = -25
J = 25

Substituting the value of J in equation 3, we get:
L = 25 - 15
L = 10

Finally, substituting the values of J and L in equation 2, we can solve for A:
3A - 25 = -10
3A = 15
A = 5

Therefore, Arun is currently 5 years old. Hence, the correct answer is option B.

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