Question

Q3. A farmer borrowed rupees 2600 at 20 % per annum. At the end of three
years, he cleared his account by paying rupees 2000 and a tractor. Find the cost
of a tractor.​

Answer 1

Concept :

• Here, in the above question, the concept of Simple Interest has been used. Where, Principal, Rate & Time are given. And also amount of money paid has been provided. Thereby, we are asked to calculate the Cost Price of the tractor.

____________________________________

Given :

• Principal (P) = Rs. 2600
• Rate (R) = $15\%$
• Time (T) = 3 years
• Amount of money paid = Rs. 2000

To Find :

• Cost of the tractor?

Method :

Firstly we'll calculate the simple interest by using this formula :-

• $\boxed {\sf{ SI \: = \dfrac{(P \times R \times T)}{100} }}$

After calculating the simple interest of the tractor. We'll find the total amount by using this formula :-

• $\boxed {\sf{ Amount = Simple \: Interest + Principal }}$

And lastly A/Q, we'll find the cost of the tractor.

Calculation :

~ Calculating the simple interest of the tractor :

$\sf{\longrightarrow SI \: = \dfrac{P \times R \times T}{100}} \\ \\ \\ \sf{\longrightarrow SI \: = \: \dfrac{2600 \times 15 \times 3}{100} } \\ \\ \\ \sf \: \longrightarrow \: SI = 26 \times 15 \times 3 \\ \\ \\ \longrightarrow \underline{\boxed{\bf{SI \: = \: \: Rs. \: 1170 }}} \: \red{\bigstar}$⠀

⠀

• Therefore, Simple Interest (SI) for the tractor is Rs. 1170.

~ Calculating the total amount for the tractor :

$\sf{\longrightarrow Amount \: = Simple \: Interest + Principal } \\ \\ \\ \sf{\longrightarrow Amount \: = \: Rs. \: 1170 + Rs. \: 2600 } \\ \\ \\ \sf \ \longrightarrow \underline{\boxed{\bf{Amount \: = \: \: Rs. \: 3770 }}} \: \pink{\bigstar}$⠀

• Therefore, total amount of money paid (A) for the tractor is Rs. 3770.

$\dag$ According to the Question,

Let's calculate the final result (Cost price) of the tractor.

So,

• [Cost Price = Total amount - Total amount of money paid. ]

Here,

• Total amount is Rs. 3770
• Total amount of money paid is Rs. 2000

Putting the values,

$\sf{\longrightarrow C.P. \: = Rs. \: 3770 - Rs. \: 2000 } \\ \\ \\ \sf \ \longrightarrow \underline{\boxed{\bf{C.P. \: = \: \: Rs. \: 1770 }}} \: \purple{\bigstar}$⠀

$\therefore$ Hence, cost price of the tractor is Rs. 1770.