A moneylender 's income decreased by Rs.60 when the rate of interest dropped from 8%p.a to 31/4%p.a.What was his principal
X* 8*1/ 100 - x*31*1/400=60
32x-31x = 60*400
X =24000
Let's denote the principal as "P".
Given:
Rate of interest before = 8% p.a
Rate of interest after = 3 1/4% p.a
Decrease in income = Rs. 60
To find the principal, we can use the formula:
Principal * Rate of interest before = Principal * Rate of interest after + Decrease in income
Plugging in the values:
P * 8/100 = P * 3.25/100 + 60
Simplifying the equation:
8P/100 = 3.25P/100 + 60
Multiply both sides by 100 to get rid of the denominators:
8P = 3.25P + 6000
Subtract 3.25P from both sides:
8P - 3.25P = 6000
4.75P = 6000
Divide both sides by 4.75:
P = 6000 / 4.75
P ≈ 1263.16
Therefore, the principal was approximately Rs. 1263.16.
To find the principal, we need to use the formula for simple interest:
Simple Interest (SI) = (Principal * Rate * Time) / 100
Let's assume the principal is P.
Given that the interest rate dropped from 8% p.a. to 3 1/4% p.a., we can determine the interest amount for both cases:
Interest1 = (P * 8 * 1) / 100 (for 8% p.a)
Interest2 = (P * 3.25 * 1) / 100 (for 3 1/4% p.a)
According to the information provided, there is a decrease of Rs. 60 in income. So we can set up the equation:
Interest1 - Interest2 = 60
((P * 8 * 1) / 100) - ((P * 3.25 * 1) / 100) = 60
Now, let's solve this equation to find the value of P, the principal.
assuming we are talking about 1 year's income,
.08p - .0325p = 60
p = 1263.20