A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time (i) the length of the shadow cast by another pole 10 m 50 cm high (ii) the height of a pole which casts a shadow 5 m long.

Here height of the pole and length of the shadow are in direct proportion.
And 1 m = 100 cm
5 m 60 cm = 5 x 100 + 60 = 560 cm
3 m 20 cm = 3 x 100 + 20 = 320 cm
10 m 50 cm = 10 x 100 + 50 = 1050 cm
5 m = 5 x 100 = 500 cm
(i). Let the length of the shadow of another pole be x.

Height of pole (in cm) 560 1050
Length of shadow (in cm) 320 x

∴ 560/320 = 1050/x ⇒ xX560 = 1050 x 320 ⇒ x=1050×320/560 = 600cm = 6m
Hence, the length of the shadow of another pole is 6 m.
(ii). Let the height of the pole be x.

Height of pole (in cm) 560 x
Length of shadow
(in cm) 320 500

∴ 560/320 = x/500 ⇒ xX320 = 560×500 ⇒ x=560X500/320 = 875 cm = 8 m 75 cm
Hence, the height of the pole is 8 m 75 cm.

Class 8 Maths Chapter 11 Exercise 13.1 Solution in Video

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