There are 351 gold coins that are supposed to be divided among Abhay, Vishal and Kishore in the ratio 2 : 3 : 4 but by mistake it was divided in the ratio of 1/2 : 1/3 : 1/4. The number of extra/deficit gold coins incurred to Abhay due to this mistake is?

Solution

Given:
– The correct ratio for dividing the gold coins among Abhay, Vishal, and Kishore is 2:3:4.
– The mistaken ratio used for division is 1/2:1/3:1/4.
– There are a total of 351 gold coins.

Step 1: Calculate the number of coins each person should have received

Total parts in the correct ratio = 2 + 3 + 4 = 9 parts

– Abhay’s share in the correct ratio: \(\frac{2}{9} \times 351 = 78\) coins
– Vishal’s share in the correct ratio: \(\frac{3}{9} \times 351 = 117\) coins
– Kishore’s share in the correct ratio: \(\frac{4}{9} \times 351 = 156\) coins

Step 2: Calculate the number of coins each person received due to the mistake

Total parts in the mistaken ratio = 1/2 + 1/3 + 1/4 = 6/12 + 4/12 + 3/12 = 13/12 parts

– Abhay’s share in the mistaken ratio: \(\frac{1/2}{13/12} \times 351 = \frac{6}{13} \times 351 = 162\) coins
– Vishal’s share in the mistaken ratio: \(\frac{1/3}{13/12} \times 351 = \frac{4}{13} \times 351 = 108\) coins
– Kishore’s share in the mistaken ratio: \(\frac{1/4}{13/12} \times 351 = \frac{3}{13} \times 351 = 81\) coins

Step 3: Calculate the number of extra/deficit gold coins incurred to Abhay due to the mistake

Extra/deficit coins for Abhay = Abhay’s share in the mistaken ratio – Abhay’s share in the correct ratio
\[ = 162 – 78 = 84 \text{ coins} \]

Conclusion

The number of extra gold coins incurred to Abhay due to the mistake is 84 coins.