Mrs. Richi Rich inherits 3224 gold coins and divides them amongst her 3 daughters Lalita, Palita and Salita in a certain ratio. Out of the total coins each of them received, Lalita sells her 50 coins, Palita donates 85 of her coins and Salita makes jewellery out of her 39 coins. Now the ratio of gold coins with them is 24 : 21 : 16 respectively. How many coins did Lalita receive from her mother? (Bank Recruitment, 2009)

### Concept & Deductions in Ratios When a total quantity is divided in an unknown initial ratio, but exact deductions are given leading to a known final ratio, first subtract the total deductions from the initial total to find the value of the new ratio parts. ### Step-by-Step Solution * **Find the Total Deductions:** Coins removed = (Lalita's sold coins) + (Palita's donated coins) + (Salita's jewellery coins) Total Deductions = $50 + 85 + 39 = 174$ coins. * **Find the Remaining Total:** Remaining coins = Total initial coins - Total Deductions Remaining coins = $3224 - 174 = 3050$ coins. * **Distribute the Remaining Total:** The remaining coins are in the ratio of $24 : 21 : 16$. Total ratio parts = $24 + 21 + 16 = 61$ parts. Value of $1$ part = $\frac{3050}{61} = 50$ coins. * **Calculate Lalita's Original Share:** Lalita's remaining share = $24 \text{ parts} \times 50 = 1200$ coins. Lalita's original share = (Lalita's remaining share) + (Lalita's sold coins) Lalita's original share = $1200 + 50 = 1250$ coins. ### Exam Strategy & Shortcut Subtract all deductions at once ($174$) from the total ($3224$) to get $3050$. Divide by the sum of the new ratio parts ($61$) to get a multiplier of $50$. Multiply Lalita's ratio part ($24$) by $50$ to get $1200$. Add her $50$ deducted coins back. Calculation: $(24 \times \frac{3224 - 174}{24+21+16}) + 50 = 1250$. ### Common Pitfall Forgetting to add back the deducted coins (in Lalita's case, the $50$ coins she sold) to find the original amount she received, leading to incorrectly selecting 1200 (Option c). ### Final Answer Therefore, the correct answer is **1250**.