‘A’, ‘B’ and ‘C’ started their independent businesses with equal amounts of capital. During the first year ‘A’ made 10% profit, ‘B’ incurred 10% loss and ‘C’ made a profit of 5%. In the second year ‘A’ incurred 20% loss, ‘B’ made profit of 20% and ‘C’ made profit of 5%. Which of the following is FALSE at the end of second year ?
A’s capital = P + 10% of P = 1.1P
B’s capital = P – 10% of P = 0.9P
C’s capital = P + 5% of P = 1.05P
At the end of the second year:
A’s capital = 1.1P – 20% of 1.1P = 1.1P * (1 – 0.20) = 1.1P * 0.80 = 0.88P
B’s capital = 0.9P + 20% of 0.9P = 0.9P * (1 + 0.20) = 0.9P * 1.20 = 1.08P
C’s capital = 1.05P + 5% of 1.05P = 1.05P * (1 + 0.05) = 1.05P * 1.05 = 1.1025P
Comparing the capitals at the end of the second year:
C (1.1025P) > B (1.08P) > A (0.88P).
So, C is the richest, B is the second richest, and A is the poorest.
Let’s evaluate the statements:
A) ‘C’ is the richest: C’s capital (1.1025P) is the highest. This is TRUE.
B) ‘A’ is the poorest: A’s capital (0.88P) is the lowest. This is TRUE.
C) ‘B’ is the richest: B’s capital (1.08P) is not the highest (C is higher). This is FALSE.
D) ‘C’ is richer than ‘B’: C’s capital (1.1025P) is greater than B’s capital (1.08P). This is TRUE.
The statement which is FALSE at the end of the second year is ‘B’ is the richest.