Question

Eesha walks 4 km due north and then 3 km due east to reach Anu's place. From Anu's place, both of them walk 4 km due north and then 3 km due east. How far are both Eesha and Anu from their respective starting points?

• A. 10 km, 5 km
• B. 5 km, 10 km
• C. 25 km, 5 km
• D. 5 km, 25 km

Answer 1

The correct option is A

10 km, 5 km

Eesha walks 4 km due north, from A to B & then 3 km due east, from B to C, to reach Anu's place at C. They both walk 4 km due north from C to D and again 3 km due east, from D to E. We see that Eesha has walked a straight distance of AC + CE from her starting point and Anu has walked a straight distance of CE from her starting point.
For $△ABC,$
$A{B}^2+B{C}^2=A{C}^2\left(usingPythagorastheorem\right)$
$\Rightarrow A{C}^2=4^2+3^2=16+9=25$
$\Rightarrow AC=5Km$

Similarly, for $△CDE$,
$C{D}^2+D{E}^2$=$C{E}^2$
$\Rightarrow$ $C{E}^2$=$4^2+3^2$=$16+9=25$
$\Rightarrow$ $CE$=$5km$
$\therefore$ AC + CE = 5 + 5 = 10 km
$\therefore$ $\text{Eesha is 10 km far from her starting point and Anu is 5 km far from her starting point.}$