Question

A wrist watch loses 10 seconds in every 8 hours. In how much time in hours will it lose 5 seconds?

Answer 1

Hint: To solve this we need to make use of a unitary method to find the amount of hours it takes to lose 5 seconds. This is because the quantities (that is the seconds lost in a wrist watch and amount of time in hours it takes to do so, are directly related). Thus, in this question, we will find the amount of hours it takes to lose 1 second and then proceed from thereon.

Complete step-by-step answer:
We are given that a wrist watch loses 10 seconds in every 8 hours. Further we have to find the amount of time it takes to lose 5 seconds. In these types of problems, we make use of unitary methods. Basically, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple. To explain this definition,
Let’s say, 2 bags cost 50 rupees and suppose we want to know how many bags we can buy from 75 rupees. What we do is, we see how many bags can be bought for 1 rupee. Then we multiply that by 75. Thus,
For 50 rupees, we have 2 bags
For 1 rupee, we have $\dfrac{1}{25}$bags
For 75 rupees, we have $\dfrac{75}{25}$=3 bags
We use a similar methodology to solve the given problem in hand.
Thus, coming back to the question, we have,
10 seconds are lost in 8 hours.
Thus, in 1 second, $\dfrac{8}{10}$ = 0.8 hours are lost.
Thus, in 5 seconds, 0.8$\times $5 = 4 hours are lost.

Note: The use of unitary method is only applicable when the quantities are directly related to each other. In case a quantity is directly related to square/cube/inverse or any other operations, the unitary method yields inaccurate results. For example, if x varies as a square of y, we cannot use unitary methods between x and y variables.