
Shortcut Trick
Ratio of A, B, and C = 1/2 : 1/3 : 3/4
Multiply the ratio by the LCM of denominators (2, 3, 4) = 12 → 6 : 4 : 9
Total units = 6 + 4 + 9 = 19 units
19 units = Rs 3800 → 1 unit = Rs 200
Share of C = 9 units × 200 = Rs. 1800
∴ The correct answer is Rs. 1800.

Alternate Method
Given: Total sum = Rs 3800, Ratio of A : B : C = 1/2 : 1/3 : 3/4.
Formula Used: Share of C = (C’s ratio unit ÷ Sum of ratio units) × Total Amount

⇒ Simplified Ratio = (1/2 × 12) : (1/3 × 12) : (3/4 × 12)
⇒ A : B : C = 6 : 4 : 9
⇒ Sum of ratio units = 6 + 4 + 9 = 19
⇒ 19 units = Rs. 3800
⇒ 1 unit = 3800 ÷ 19 = Rs. 200
⇒ Share of C = 9 units × 200 = Rs. 1800
⇒ This matches the value given in option (4).
∴ The correct answer is Rs. 1800.

Additional Information
Simplifying Fractional Ratios
To convert a fractional ratio a/b : c/d into simplest form, multiply both terms by the LCM of denominators b and d.
Proportional Division
If a sum X is divided in the ratio a : b : c, then the share of C is calculated as [c / (a + b + c)] × X.
Compound Ratio
For two ratios a : b and c : d, the compound ratio is (a × c) : (b × d).