Question

One day, Manisha covered a distance of $24$ km at $x$ km/hr and another $40$ km at $y$ km/hr. Next day, she covered $18$ km at $x$ km/hr and another $48$ km at $y$ km/hr. If each day she took $9$ hours to complete her journey find the values of $x$ and $y$.

• A. $x=7$ and $y=12$
• B. $x=6$ and $y=8$
• C. $x=2$ and $y=5$
• D. $x=17$ and $y=3$

Answer 1

The correct option is B $x=6$ and $y=8$

Since,
Time $=\frac{Distance}{Speed}$
Total time taken both the days, $\frac{24}{x}+\frac{40}{y}=\frac{18}{x}+\frac{48}{y}=9$
Considering $\frac{24}{x}+\frac{40}{y}=\frac{18}{x}+\frac{48}{y}$ and simplifying it we get $y=\frac{4x}{3}$
Also, considering $\frac{24}{x}+\frac{40}{y}=9$ and substituting $y=\frac{4x}{3}$ in it, we get

$\frac{24}{x}+\frac{40\times 3}{4x}=9$

$\Rightarrow \frac{24}{x}+\frac{10\times 3}{x}=9$

$\Rightarrow \frac{54}{x}=9$

$\Rightarrow x=6$
And $y=\frac{4x}{3}=8$