Question

How much time did X take to reach the destination?
I. The ratio between the speed of X and Y is 3:4.
II. Y takes 36 minutes to reach the same destination.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer

Answer 1

Hint: To solve this question first we will collect the information given in question to find the time taken by X. Then we will find the time taken by X by assuming that X & Y has common distance by taking distance formula i.e. $\text{Distance=}\dfrac{\text{Speed}}{\text{Time}}$ . Then we will select the option according to the information being used to find the time of X.

Complete step by step solution:
In statement I, it is given that the ratio between the speed X and Y is $3:4$ .
i.e. $X:Y=3:4$
We can also write it as –
$\dfrac{\text{Speed of X}}{\text{Speed of Y}}=\dfrac{3}{4}$ ………….. (1)
Let us assume the common distance taken by both X and Y is ‘d’.
In statement II it is given that Y takes 36 minutes to reach the same destination.
$\therefore Y=36$ minutes.
Now, we will find the time taken by X.
Let us consider the time taken by X be ‘t’.
We know that $\text{Speed=}\dfrac{\text{distance}}{\text{time}}$ .
By substituting this in the in the equation (1), we get –
$\dfrac{\text{Speed of X}}{\text{Speed of Y}}=\dfrac{3}{4}$
$\Rightarrow \dfrac{\dfrac{d}{t}}{\dfrac{d}{36}}=\dfrac{3}{4}$
By taking the reciprocal of denominator, we get –
$\Rightarrow \dfrac{d}{t}\times \dfrac{36}{d}=\dfrac{3}{4}$ .
By cancelling the common factor from the numerator and denominator, we get –
$\Rightarrow \dfrac{36}{t}=\dfrac{3}{4}$
By simplifying the above equation and taking ‘t’ one side, we get –
$\begin{aligned} & \Rightarrow t=\dfrac{36\times 4}{3} \\\ & \Rightarrow t=48 \\\ \end{aligned}$
Therefore, time taken by X is $t=48$ minutes.
So, to solve the answer we need both the ratio between the speed of X & Y and the time taken by Y to find the time taken by X.
Hence, Option (E) is the correct answer.

Note: Here, students may make mistakes while selecting the correct option. They should understand the information given in the question to solve this answer. The question consists of 2 statements in which the speed of X and Y is given in statement I and time taken by y to reach the destination in statement II. Students need to decide whether the data provided in the statements are sufficient. As in this case both the statements are sufficient to solve this problem, students have to select the option correctly.