1. The amount Rs 2100 became Rs 2352 in 2 years at simple interest. If the interest rate is decreased by 1%, what is the new interest?
2. My grandfather was 9 times older than me 16 years ago. He will be 3 times of my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was?
Pls help me
At interest rate x,
2100(1+2x) = 2352
x = (2352/2100 - 1)/2 = .06 = 6%
so, x-1 = 5%
My age=m
grandfather is g
(g-16) = 9(m-16)
(g+8) = 3(m+8)
so, solve for m and g, and you want
(m-8)/(g-8) = ?
Sure! I'd be happy to help you with both questions.
1. To calculate the new interest, we first need to calculate the original interest. We can use the simple interest formula:
Simple Interest = Principal * Rate * Time.
Given that the Principal (P) is Rs 2100, Time (T) is 2 years, and the Simple Interest (SI) is Rs 2352 - Rs 2100 = Rs 252.
Plugging these values into the formula, we can solve for the Rate (R):
252 = 2100 * R * 2.
Dividing both sides by 4200, we have:
R = 252 / 4200.
≈ 0.06.
Therefore, the original interest rate is 0.06 or 6%.
Now, to calculate the new interest after decreasing the rate by 1%, we simply subtract 1% (0.01) from the original rate:
New Interest Rate = 6% - 1%
= 0.06 - 0.01
= 0.05 or 5%.
So, the new interest rate is 5%.
2. Let's break down the problem step by step.
Let "M" represent your age and "G" represent your grandfather's age.
16 years ago, your grandfather was 9 times older than you, so we have the equation:
G - 16 = 9 * (M - 16).
Simplifying this equation, we get:
G - 16 = 9M - 144.
Rearranging the terms, we have:
G - 9M = -144 + 16,
G - 9M = -128. ----(Equation 1)
8 years from now, your grandfather will be 3 times your age, so we have:
G + 8 = 3 * (M + 8).
Simplifying this equation, we get:
G + 8 = 3M + 24.
Rearranging the terms, we have:
G - 3M = 24 - 8,
G - 3M = 16. ----(Equation 2)
Now, let's solve the system of equations (Equation 1 and Equation 2) to find the ratio of your age to that of your grandfather eight years ago.
Multiplying Equation 1 by 3 and Equation 2 by 9, we get:
3G - 27M = -384, ----(Equation 3)
9G - 27M = 144. ----(Equation 4)
Subtracting Equation 3 from Equation 4, we eliminate the "M" term:
(9G - 27M) - (3G - 27M) = 144 - (-384),
9G - 27M - 3G + 27M = 144 + 384,
6G = 528.
Dividing both sides by 6, we find:
G = 88.
Now, substituting the value of G into Equation 2, we can solve for M:
G - 3M = 16,
88 - 3M = 16,
-3M = 16 - 88,
-3M = -72.
Dividing both sides by -3, we get:
M = 24.
Therefore, your age is 24 and your grandfather's age is 88.
Eight years ago, your age was 24 - 8 = 16, and your grandfather's age was 88 - 8 = 80.
So, the ratio of your age to that of your grandfather eight years ago is:
Ratio = Your Age / Grandfather's Age.
= 16 / 80
= 1 / 5.
Therefore, the ratio of your age to that of your grandfather eight years ago was 1:5.