₹ 1087 is divided among $A, B$ and $C$ such that if ₹ 10, ₹ 12 and ₹ 15 are diminished from the shares of $A, B$ and $C$ respectively, the remainders will be in the ratio of $5, 7$ and $9$. What is the share of $B$?

### Concept & Adjusted Total Similar to problems with increased shares, when amounts are diminished (subtracted), you must subtract the total diminished amount from the overall total to find the base that corresponds to the given ratio. ### Step-by-Step Solution Given: Total initial amount = ₹ 1087 Decreases: $A$ by ₹ 10, $B$ by ₹ 12, $C$ by ₹ 15 Ratio of remainders = $5 : 7 : 9$ 1. Find the new total after all deductions are made: Total deduction = $10 + 12 + 15 = 37$ New Total (sum of remainders) = $1087 - 37 = 1050$ 2. Distribute the new total (₹ 1050) according to the ratio of remainders ($5 : 7 : 9$). Total ratio parts = $5 + 7 + 9 = 21$ Value of 1 part = $\frac{1050}{21} = 50$ 3. Calculate the remainder share for $B$: Remainder of $B$'s share = $7 \text{ parts} = 7 \times 50 = 350$ 4. Find the original share of $B$ by adding back its specific deduction: Original share of $B = 350 + 12 = 362$ ### Exam Strategy & Shortcut To find just $B$'s share rapidly: Original $B$ = $\left(\frac{7}{5+7+9} \times (1087 - (10+12+15))\right) + 12$ Original $B = \left(\frac{7}{21} \times 1050\right) + 12 = 350 + 12 = 362$. ### Common Pitfall Forgetting to add back the diminished amount (₹ 12) at the final step, leading to mistakenly selecting a distractor option (like 350 if it were present). ### Final Answer Therefore, the correct answer is **₹ 362**.