# 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 5m long.

**Solution:**

Given that, a 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long.

i) Length of the shadow cast by another pole 10 m 50 cm high.

Height of the pole |
Length of the shadow |

5.6 m | 3.2 m |

10.5 m | ? |

Let the height of the pole be x and the length of the shadow be y

As the height of the pole increases the length of the shadow also increases. So, it is a direct proportion.

Two numbers x and y are said in direct proportion if, the relationship between two quantities is such that if we increase one, the other will also increase, and if we decrease one the other quantity will also decrease.

x/y = k, x = ky

where k is a constant.

Thus, x₁_{ }/ y₁ = x₂ / y₂

5.6 / 3.2 = 10.5 / y₂

5.6 × y₂ = 10.5 × 3.2

y₂ = (10.5 × 3.2) / 5.6

y₂ = 6

If the height of the pole is 10.5 m, then the length of the shadow is 6 m.

(ii) The height of the pole which casts a shadow of 5 m long.

x₁_{ }/ y₁_{ }= x₂_{ }/ y₂

5.6 / 3.2 = x₂_{ }/ 5

3.2 x₂_{ }= 5 × 5.6

x₂ = (5 × 5.6) / 3.2

x₂ = 8.75

If the length of the shadow is 5 m, then the height of the pole is 8.75 m.

**Video Solution:**

## 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 5m long

### Maths NCERT Solutions Class 8 - Chapter 13 Exercise 13.1 Question 9

**Summary:**

A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. i) If the height of the pole is 10.5 m, then the length of the shadow is 6 m. (ii) If the length of the shadow is 5 m, then the height of the pole is 8.75 m.