JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Heights and Distances

Two vertical poles

AB = 15 m

and

CD = 10 m

are standing apart on a horizontal ground with points

A

and

C

on the ground. If

P

is the point of intersection of

B C

and

A D

, then the height of

P

(in

m

) above the line

A C

is:

(A) $\frac{10}{3}$
(B)6✓ Correct
(C)5
(D) $\frac{20}{3}$

Answer: (B)

Solution

Let the two poles stand a horizontal distance apart and let

P

be the height at which the cross-lines

B C

and

A D

meet. From similar triangles, the line from the top of the

15

m pole contributes

\frac{h}{15}

of the base and the line from the top of the

10

m pole contributes

\frac{h}{10}

of the base, and these two parts make up the whole base, so

\frac{h}{15} + \frac{h}{10} = 1

. Then

\frac{2 h + 3 h}{30} = 1

, giving

5 h = 30

and

h = 6

JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Single correct option

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