Q.A invests $5000$ rupees for $4$ months and B invests $4000$ rupees for $5$ months. Their profits should be divided in the ratio:

With different times, the ratio is that of capital x time, not of the capitals alone.

The times differ, so profit is divided in the ratio of capital × time (a compound partnership), not by the capitals alone.

Capital-months. $A: 5000 \times 4 = 20000, \qquad B: 4000 \times 5 = 20000.$

Ratio. $20000 : 20000 = 1 : 1.$

Checking the options. Option (b) $5:4$ is the ratio of the capitals alone ($5000:4000$), which ignores the time — a classic distractor. Option (c) $4:5$ is the ratio of the times alone ($4$ months to $5$ months), which ignores the capital. Option (d) $25:16$ is the ratio of the squares of the capi …

The two most tempting wrong answers, (b) $5:4$ and (c) $4:5$, come from using only the capitals or only the times. In a compound partnership neither is correct on it …