Proportional Division — Prelims Questions

Three partners A, B, and C invested ₹40,000, ₹60,000, and ₹80,000 respectively in a business. After 8 months, A withdrew ₹10,000, and after 10 months, B invested an additional ₹20,000. If the total profit at the end of the year is ₹54,000, what is C's share?

A sum of ₹7,200 is to be divided among A, B, and C in the ratio 2:3:4. However, A receives ₹200 less than his entitled share, and this amount is distributed equally between B and C. What is the final amount received by B?

In a factory, work is distributed among three machines A, B, and C based on their efficiency. If A can complete the work in 12 days, B in 15 days, and C in 20 days, and the total payment for the work is ₹47,000, how much should machine A receive?

A father wants to distribute his property worth ₹12,60,000 among his four children in the ratio of their ages. If the ages are 18, 21, 24, and 27 years, and the eldest child donates ₹30,000 to charity before receiving his share, what amount does the eldest child finally receive?

Three cities A, B, and C are to receive government funds in the ratio 5:7:8 based on their population. However, due to a natural disaster, city A receives an additional 20% of its allocated share, while cities B and C receive their shares reduced by 5% each. If the total fund is ₹40,00,000, what is the final amount received by city A?