Question

In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the actual ship is 28 m, then find the length of the model ship?
(a) 19
(b) 14
(c) 17
(d) 21

Answer 1

Hint: We first find the representative fraction (1m on actual ship: ___m in the model ship) by using the heights of mast in model ship and actual ship which were given in the problem. We use this representative and length of the ship given in the problem to find the length of the model ship.

Complete step-by-step answer:
Given that we have a model representing an actual ship. The height of the mast in the actual ship is 12 m high and the mast of the model ship is 9 cm high. We need to find the length of the model ship, if the length of the actual ship given is 28 m.
We have got a 9 cm mast in the model ship = 12 m mast in the actual ship.
We know that 1 cm = 0.01 m. We get 9 cm = 0.09 m. We use this to convert the dimension of the mast of the model ship into meters.
1we have got 0.09 m in the model ship = 12 m in the actual ship.
We have 1m in actual ship = $ \dfrac{0.09}{12} $ m in model ship.
We have 1 m in the actual ship = $ \dfrac{0.03}{4} $ m in model ship ---(1).
We use this notation to find the length of the model ship. We have the length of the model ship given as 28 m.
Using equation (1) we get,
We have 28 m in the actual ship = $ \dfrac{0.03}{4}\times 28 $ m in the model ship.
We have 28 m in the actual ship = $ 0.03\times 7 $ m in the model ship.
We have 28 m in actual ship = 0.21m in model ship.
We know that 1 cm = 0.01 m. We get 0.21m = 21 cm.
We have 28 m in actual ship = 21 cm in model ship.
∴ The length of the model ship is 21 cm.
So, the correct answer is “Option D”.

Note: We should not make mistakes while converting dimensions from centimeters to meters. We first get lent hog the model ship in meters, but the length of the model ship is in centimeters, so we converted them in centimeters. Similarly, we expect the problems to find the area of the base of the ship.