Explanation:

Let Shyam's present age = S

Let Ram's present age = R

- Four years ago: Shyam's age = S - 4, Ram's age = R - 4

- Given: S - 4 = (3/4)(R - 4)

- Four years hence: Shyam's age = S + 4, Ram's age = R + 4

- Given: S + 4 = (5/6)(R + 4)

Let's solve:

From (1): S - 4 = (3/4)(R - 4)

? 4(S - 4) = 3(R - 4)

? 4S - 16 = 3R - 12

? 4S - 3R = 4 ...(a)

From (2): S + 4 = (5/6)(R + 4)

? 6(S + 4) = 5(R + 4)

? 6S + 24 = 5R + 20

? 6S - 5R = -4 ...(b)

Now, solve equations (a) and (b):

Multiply (a) by 5: 20S - 15R = 20

Multiply (b) by 3: 18S - 15R = -12

Subtract second from first:

(20S - 15R) - (18S - 15R) = 20 - (-12)

2S = 32 ? S = 16

- Option 3: 16 years (human calculation matches equations)

- Option 1: 24 years (too high)

- Option 2: 20 years (not matching)

- Option 4: 15 years (too low)

Correct answer: Option 3 — 16 years