Suppose a company needs a computer for some period of time. The company can either hire a computer for ₹ 2,000 per month or buy one for ₹ 25,000. If the company has to use the computer for a long period, the company will pay such a high rent, that buying a computer will be cheaper. On the other hand, if the company has to use the computer for say, just one month, then hiring a computer will be cheaper. Find the number of months beyond which it will be cheaper to buy a computer.

Step 1 : Formulation :

The relevant factors are the time period for hiring a computer and the two costs given to us. We assume that there is no significant change in the cost of purchasing or hiring the computer. So, we treat any such change as irrelevant. We also treat all brands and generations of computers as the same, i.e., these differences are also irrelevant. The expense of hiring the computer for x months is ₹ 2000x. If this becomes more than the cost of purchasing a computer, we will be better off buying a computer. So, the equation is:

⇒ 2000x = 25000 …….(1)

Step 2 : Finding the solution :

By solving equation (1), we get :

⇒ x = $\dfrac{25000}{2000} = \dfrac{25}{2}$ = 12.5

Step 3 : Interpretation :

Since x = 12.5

Hence, after 12.5 months it will be cheaper to buy a computer.