Mr Tony and his wife used 6,000 naira on a business, the business was valued and sold for 18,000. When a VAT of 3% was removed, the remaining gain was shared in ratio 2:3 between Mr Tony and his wife respectively. By what amount was Mr Tony's wife gain higher than that of her husband?
To find the amount by which Mr Tony's wife's gain was higher than his, let's break down the problem step by step.
Step 1: Calculate the initial investment
Mr Tony and his wife initially used 6,000 naira as their investment in the business.
Step 2: Calculate the selling price after VAT is removed
VAT is 3% of the selling price, so we need to subtract 3% from 18,000 naira to find the actual selling price after VAT is removed.
VAT = (3/100) * 18,000 = 540 naira
Selling price after VAT = 18,000 - 540 = 17,460 naira
Step 3: Calculate the gain
The gain is the selling price after VAT minus the initial investment.
Gain = Selling price after VAT - Initial investment
Gain = 17,460 - 6,000 = 11,460 naira
Step 4: Calculate the shares of Mr Tony and his wife
The shares are divided in a ratio of 2:3 between Mr Tony and his wife.
Total ratio = 2+3 = 5
Mr Tony's share = (2/5) * Gain = (2/5) * 11,460 = 4,584 naira
His wife's share = (3/5) * Gain = (3/5) * 11,460 = 6,876 naira
Step 5: Calculate the difference in gains
To find the amount by which Mr Tony's wife's gain is higher than his, subtract Mr Tony's share from his wife's share.
Difference = Wife's share - Tony's share
Difference = 6,876 - 4,584 = 2,292 naira
Therefore, Mr Tony's wife's gain was higher than his by 2,292 naira.