Question

If Rs. 1250 amounts to Rs. 1550 in 3 years at simple interest, what will Rs. 3200 amount to in 4 years at the same rate?

Answer 1

Hint: In this problem, we have to find simple interest with the given principal and number of days, to find the total amount at the end of 4 years. We are already given interest, principal amount and number of days with which we have to find the rate, to find the interest for the given amount. We should know some formulas to solve these types of problems.

Complete step by step answer:
We know that the formula for interest from which we can find the rate is,
Interest = \[\dfrac{\text{Principle amount}\times \text{Number of days}\times \text{Rate}}{100}\] …… (1)
We know that the given interest is Rs. 1250 amount to Rs. 1550 in 3 years at the principal amount Rs. 1250. we can substitute these given data in the above formula, we get
\[\Rightarrow \left( 1550-1250 \right)=\dfrac{1250\times 3\times Rate}{100}\]
Now we can subtract the left-hand side and write the above step as,
\[\Rightarrow \text{Rate = }\dfrac{300\times 100}{1250\times 3}\]
We can simplify the above step, we get
\[\Rightarrow \text{Rate = 8}\]
We have to find the interest for the principal amount Rs. 3200 whose rate is 8 and number of days is 4 years. We can substitute these data in the formula (1), we get
\[\Rightarrow \text{Interest = }\dfrac{3200\times 4\times 8}{100}=1024\]
Now we can add the above interest and the principle amount.
\[\Rightarrow 1024+3200=4224\]

Therefore, the total amount is Rs. 4224.

Note: Students make mistakes, while finding the simple interest, we have to subtract the principal amount and the amount after interest to get the simple interest. We should know some formulas to be remembered and to solve these types of problems.