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a banker lends rs. 2,000 at simple interest to a customer. the rate of interest for the first year is x%, for the second year it is (x + 2)%, for the third year it is (x + 4)% and so on. at the end of the fifth year, if the total simple interest accrued is rs. 1500, find the value of x.
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a banker lends rs. 2,000 at simple interest to a customer. the rate of...
Problem:
A banker lends rs. 2,000 at simple interest to a customer. The rate of interest for the first year is x%, for the second year it is (x+2)%, for the third year it is (x+4)% and so on. At the end of the fifth year, if the total simple interest accrued is rs. 1500, find the value of x.
Solution:
Let's break down the problem into different parts:
Step 1: Calculate Simple Interest for Each Year
The formula for calculating simple interest is:
Simple Interest = (P * R * T) / 100
Where,
- P = Principal amount (Rs. 2,000 in this case)
- R = Rate of interest
- T = Time period (in years)
Using the given information, we can calculate the simple interest for each year:
- Simple Interest for Year 1 = (2000 * x * 1) / 100 = 20x
- Simple Interest for Year 2 = (2000 * (x+2) * 1) / 100 = 20(x+2)
- Simple Interest for Year 3 = (2000 * (x+4) * 1) / 100 = 20(x+4)
- Simple Interest for Year 4 = (2000 * (x+6) * 1) / 100 = 20(x+6)
- Simple Interest for Year 5 = (2000 * (x+8) * 1) / 100 = 20(x+8)
Step 2: Add Up Simple Interest for All Years
Now, we can add up the simple interest for all years to get the total simple interest:
Total Simple Interest = 20x + 20(x+2) + 20(x+4) + 20(x+6) + 20(x+8)
Simplifying the above equation, we get:
Total Simple Interest = 100x + 200
Step 3: Find the Value of x
From the given information, we know that the total simple interest accrued is Rs. 1500. Therefore,
100x + 200 = 1500
100x = 1300
x = 13
Step 4: Verify the Solution
Let's verify the solution by calculating the total simple interest using the value of x we obtained:
Total Simple Interest = 20(13) + 20(15) + 20(17) + 20(19) + 20(21) = 1500
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a banker lends rs. 2,000 at simple interest to a customer. the rate of interest for the first year is x%, for the second year it is (x + 2)%, for the third year it is (x + 4)% and so on. at the end of the fifth year, if the total simple interest accrued is rs. 1500, find the value of x.
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