Question

John and Mathew started a business with their capitals in the ratio $8:5$. After $8$ months,john added $25\%$ of his earlier capital as further investment. At the same time,Mathew withdraw $20\%$ of his earlier capital. At the end of the year,they earned $Rs.52,000$ as profit.How should they divide the profit between them ?

Answer 1

Let Investment of John is $8x$

Investment of Mathew is $5x$

After $8$ months ,Investment of John is $\frac{5}{4}\times 8x=10x$

,Investment of Mathew is $\frac{4}{5}\times 5x=4x$

Profit $=52,000$

Profit for first $8$ months is $\frac{8}{12}\times 52000=34,667$

Profit to John for first $8$ months is $\frac{8}{13}\times 34667=21,333.54$

Profit to Mathew for first $8$ months is $\frac{5}{13}\times 34667=13,333.46$

Profit for last $4$ months is $\frac{4}{12}\times 52000=17,333$

Profit to John for last $4$ months is $\frac{10}{14}\times 17333=12380.95$

Profit to Mathew for last $4$ months is $\frac{4}{14}\times 17333=4952.05$

Total Profit of John is $21333.54+12380.95=33,714.49$

Total Profit of Mathew is $13333.46+4952.05=18,285.51$