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August 10th, 2019, 07:06 AM   #1
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Where I am doing wrong in this simple interest problem?

A certain sum of money at certain rate of interest becomes 2100 in 2 years at simple rate of interest and 2250 in 5 years. Find the rate of interest?

2250 corresponds to 5
2100 corresponds to 2
---------------- (subtracting)
150 corresponds to 3
?? >>> 2

100 corresponds to 2
then for 2 years; subtracting 100 from 2100 to get
principal i.e 2000. since PRINCPLE = Amount - SI.

2100 = 2000*R*2/100; R = 52.5%

But R is 2.5%. please point out my mistake.
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August 10th, 2019, 07:54 AM   #2
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1. "Corresponds to" is not a clearly defined mathematical operator. You need to define what the relationship is before you can see whether subtraction makes sense.

2. You are given the final amounts (principal plus interest). What do we know?
P + 2*R*P = 2100
P + 5*R*P = 2250

We can subtract these equations, to see that 3*R*P = 150. In other words, in three years, it earned 150 in interest. Solve for R -> R = 50/P.
Now we can substitute this value for R back into either of the other equations. I picked the first one.
P + 2*(50/P)*P = 2100
-> P = 2000
-> R = 50/P = 50/2000 = 5/200 = 2.5/100 = 2.5 %

This one is simple enough that you could do it in your head, but only if you understand what the values represent. That's what algebra is for - to help you solve problems that you can't work out easily in your head.

3. Short answer: You forgot to add/subtract the principal in your last equation.
Thanks from Ganesh Ujwal

Last edited by skipjack; August 10th, 2019 at 10:22 AM.
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August 10th, 2019, 11:25 AM   #3
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The usual procedure, given two equations, is to eliminate one of the variables, so that you can find the other.

Dividing the first equation by the second eliminates P and gives (1 + 2R)/(1 + 5R) = 2100/2250 = 14/15, where R (not R%) is the interest rate.

That simplifies to R = 1/40 = 2.5%.

In the original work, the last equation should have been 100 = 2000*R*2/100, where R% is the interest rate.

That simplifies to R = 2.5, so the interest rate is 2.5%.
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