CAT Quant Practice Problems

Question: Ramu went by car from Calcutta to Trivandrum via Madras, without any stoppages. The average speeds for the entire journey was 40 kmph. What was the average speed from Madras to Trivandrum?

I. The distance from Madras to Trivandrum is 0.30 times the distance from Calcutta to Madras.

II. The average speed from Madras to Trivandrum was twice that of the average speed from Calcutta to Madras.

1. If the question can be answered with the help of statement I alone,
2. If the question can be answered with the help of statement II alone,
3. If both, statement I and statement II are needed to answer the question, and
4. If the statement cannot be answered even with the help of both the statements.

Correct Option:3

1. If only 1st statment taken into consideration:
$y=0.30x$ (Where y= distance from Madras to Trivandrum and x= distance from Calcutta to Madras)
Nothing absolute can be said about average speed from Madras to Trivendrum.
2. If only 2nd statement taken into consideration:
$\frac{y}{t_y} = 2\frac{x}{t_x}$ ( Where tx and ty are time taken for calcutta to madras and madras to trivendrum respectively.)
And nothing absolute can be said about average speed from Madras to Trivendrum.
3. Now when both statements taken into consideration:
We will have $y=0.30x$; $\frac{y}{t_y} = 2\frac{x}{t_x}$ and $\frac{x+y}{t_x+t_y}$ = 40 (Given)
After solving above three equations we can find a unique value for average speed from Madras to Trivendrum i.e.
$\frac{y}{t_y} = \frac{920}{13}$