Question

A farmer buys a used tractor of $Rs.12000$. he pays $Rs.6000$ cash and agrees to pay the balance in annual instalment of $Rs.500$ plus $12\%$ interest on the unpaid amount. The tractor cost for farmer is ?

• A. $Rs.16680$
• B. $Rs.16670$
• C. $Rs.16650$
• D. None of these

Answer 1

The correct option is A $Rs.16680$

Given, the farmer pays a tractor of $Rs.12000$.

He pays $Rs.6000$ in cash.

Therefore, unpaid amount$=Rs.12000-Rs.6000=Rs.6000$

The interest to be paid annually is 12% of $6000$, 12% of $5500$, 12% of $5000$,...., 12% of $500$.

Thus, total interest to be paid= 12% of $6000+$12% of $5500+$12% of $5000+$.....$+$12% of $500$

$=$12% of$(6000+5500+5000+.....+500)$

$=$12% of$(500+1000+1500+....+6000)$

Since, the series is an $A.P.$ with both the first term and common difference equal to $500$.

Let, the number of terms of the $A.P.$ is $n$

$\therefore 6000=500+(n-1)500\Rightarrow 1+(n-1)=12\Rightarrow n=12$

$\therefore$ Sum of the $A.P.$

$=\frac{12}{2}\left[2\right(500)+(12-1\left)500\right]=6[1000+5500]=6\left[6500\right]=39000$

Thus, total interest to be paid$=$12% of$(500+1000+1500+...+6000)$

$=$12% of $39000$

$=Rs.4680$

$\therefore$ Tractor cost for the farmer$=(Rs.12000+Rs.4680)=Rs.16680.$