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Leaving home at the same time, Amal reaches office at $10:15$ am if he travels at $8$ km/hr, and at $9:40$ am if he travels at $15$ km/hr. Leaving home at $9:10$ am, at what speed, in km/hr, must he travel so as to reach office exactly at $10$ am?

  1. $13$
  2. $14$
  3. $12$
  4. $11$
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Let the distance between home and office be $`d\text{’} \; \text{km}.$

Time is taken to reach office.     

  • At speed of $8 \; \text{km/hr} \rightarrow 10 : 15 \; \text{AM}$
  • At speed of $15 \; \text{km /hr} \rightarrow 9 : 40 \; \text{AM}$

Time difference $ = \frac{35}{60} \; \text{hr}$

$ \Rightarrow \frac{d}{8} – \frac{d}{15} = \frac{35}{60}$

$ \Rightarrow \frac{15d – 8d}{120} = \frac{35}{60}$

$ \Rightarrow 7d = 70$

$ \Rightarrow \boxed{d= 10 \; \text{km}}$

Now,

Time $ = 50 \; \text{minutes} = \frac{50}{60} = \frac{5}{6} \; \text{hr}$

Let the speed be $`S\text{’} \;\text{km/hr}$

$ \Rightarrow S = \frac{10}{\frac{5}{6}}$

$ \Rightarrow S = \frac{10 \times 6}{5}$

$ \Rightarrow \boxed{ S = 12 \; \text{km/hr}}$

$\therefore$ The required speed $ = 12 \; \text{km/hr}$

Correct Answer $: \text{C}$

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