Rs. 782 is divided in the ratio 1/2 : 2/3 : 3/4. Find the first part.

Problem restatement
Divide Rs. 782 in the proportion 1/2 : 2/3 : 3/4 and compute the first share.

Concept/Approach
Clear the fractional ratio by multiplying each term by the LCM of denominators (12) to get an integer ratio, then apply the standard part formula.

Step-by-step calculation
(1/2 : 2/3 : 3/4) → multiply by 12 → 6 : 8 : 9Total parts = 6 + 8 + 9 = 23Value per part = 782 / 23 = 34First part = 6 × 34 = Rs. 204

Verification/Alternative
Other parts: 8 × 34 = Rs. 272; 9 × 34 = Rs. 306; sum = 204 + 272 + 306 = 782.

Common pitfalls
Adding the fractions directly or forgetting to scale them to a common denominator.

Final Answer
Rs. 204