Question

A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, the distance between his house and school is:
A. 6.5 km
B. 5.5 km
C. 5 km
D. 6 km

Answer 1

AnswEr :

6 km.

$\bf{\pink{\underline{\underline{\sf{Given\::}}}}}$

A boys goes to his school from his house at a speed of 3 km/hrs and returns at a speed of 2 km /hrs. If he takes 5 hous in going and coming.

$\bf{\pink{\underline{\underline{\sf{To\:find\::}}}}}$

The distance between his house and school.

$\bf{\pink{\underline{\underline{\sf{Explanation\::}}}}}$

Let the distance covered of boy be R

$\bf{We\:have}\begin{cases}\sf{The\:time\:taken\:for\:going\:school\:(t_{1})=\frac{R}{3} }\\ \sf{The\:time\:taken\:for\:coming\:back\:(t_{2})=\frac{R}{2} }\end{cases}}$

$\bf{\red{\underline{\underline{\tt{A.T.Q\::}}}}}$

$\Rightarrow\tt{Total\:time\:=\:t_{1}+t_{2}=5}\\\\\\\Rightarrow\tt{\dfrac{R}{3} +\dfrac{R}{2} =5\:\:\:\:\:\big[Taking\:L.C.M.\:of\:3\&\:2\big]}\\\\\\\Rightarrow\tt{\dfrac{2R+3R}{6} =5}\\\\\\\Rightarrow\tt{\dfrac{5R}{6} =5}\\\\\\\Rightarrow\tt{5R=30}\\\\\\\Rightarrow\tt{R=\cancel{\dfrac{30}{5} }}\\\\\\\Rightarrow\tt{\pink{R=6\:kilometres}}$

Thus,

∴ The distance between his house and school is 6 km.

Answer 2

Answer:

Step-by-step explanation:

as distance between them is same.

so speed is inversely propotinal to time

s1 :s2

3: 2

t1 : t2

2 : 3

multiply speed with time to find distance (s1*t1) or (s2*t2)

3*2 =6 kmph

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