Ram and shyam jointly lend out rs17261 at 20% per annum compound interest such that rams amount for 2 year is same as is the shyams amount for 5 years.by how much does rams sum exceed shyams sum?
sorry. can you please explain in detail. x(1.2)^2-x how you got this?
To solve this problem, we need to calculate the amounts each person has at the end of the given time periods.
Let's assume that Ram's initial amount is x, and Shyam's initial amount is y.
Given that Ram's amount for 2 years is equal to Shyam's amount for 5 years, we can set up the following equations:
Ram's amount after 2 years:
A = x * (1 + r/100)^t
A = x * (1 + 20/100)^2
A = x * (1.20)^2
A = 1.44x
Shyam's amount after 5 years:
B = y * (1 + r/100)^t
B = y * (1 + 20/100)^5
B = y * (1.20)^5
B = 1.488y
Given that A = B, we can equate the equations:
1.44x = 1.488y
To find the value of x/y, we can solve this equation:
1.44x = 1.488y
x/y = 1.488/1.44
Now, let's calculate the values:
x/y ≈ 1.03472
Since the question asks for the excess of Ram's amount over Shyam's amount, we can calculate it as follows:
Excess = Ram's amount - Shyam's amount
Excess = 1.44x - 1.488y
Substituting the value of x/y:
Excess = 1.44 * 1.03472y - 1.488y
Excess ≈ 0.4936y
Hence, Ram's sum exceeds Shyam's sum by approximately 0.4936 times the value of y.
Ram's amount ---- x
shyam's amount ---- 17261-x
interest earned by Ram = x(1.2)^2 - x
interest earned by shyam = ......
Ram's interest = shyam's interest
Can you follow my logic?