Three partners A, B and C divide ₹3,83,160 amongst themselves. If ₹3,700,…

When a fixed amount is removed from each person's share and the amounts that remain are given in a ratio, first find the total that is actually being divided in that ratio by subtracting the sum of all the removed amounts from the grand total. Split this reduced total into the given ratio to get each person's ratio part, then add back that person's own removed amount to get their true share.

1. Add the three amounts that are subtracted: ₹3,700 + ₹4,800 + ₹5,300 = ₹13,800.

2. Subtract this sum from the total to get the amount actually shared in the ratio 13 : 17 : 27: ₹3,83,160 − ₹13,800 = ₹3,69,360.

3. Add the ratio terms: 13 + 17 + 27 = 57.

4. Find the value of one ratio part: ₹3,69,360 ÷ 57 = ₹6,480.

5. A's ratio part is 13 units: 13 × ₹6,480 = ₹84,240.

6. Add back the ₹3,700 that was subtracted from A's share: ₹84,240 + ₹3,700 = ₹87,940.

Applying the same method to B and C confirms the total: B's share = (17 × ₹6,480) + ₹4,800 = ₹1,14,960; C's share = (27 × ₹6,480) + ₹5,300 = ₹1,80,260. Adding all three: ₹87,940 + ₹1,14,960 + ₹1,80,260 = ₹3,83,160, which matches the total given in the question.

A frequent slip is to stop at the ratio part alone and forget to add back the subtracted amount — that gives ₹84,240 instead of A's actual share, ₹87,940.