Question

A certain sum is invested for a certain time. It amounts to Rs
400 if the rate is 6% per annum. But when invested at a rate
of 2% per annum, it amounts to Rs 250. What is the sum?

Answer 1

@ganeshie8 quite similar to your name.. :P

Answer 2

Probably his brother

Answer 3

400=p*6*t//100
250=p*2*t/100

Answer 4

P will remain same..

Answer 5

And t will also be the same..

Answer 6

To find P, we have to find t also..

Answer 7

40000=3pt
12500=pt

Answer 8

Let me think, I am little bit rusty on these topics..

Answer 9

200/3+125=575/2=

Answer 10

What?

Answer 11

i dont know really

Answer 12

So Am I..

Answer 13

okay

Answer 14

Not okay,,

Answer 15

I got something for you..

Answer 16

how to do this problem

Answer 17

\[P = \frac{A_1R_1 - A_2R_2}{R_1 - R_2}\]

Answer 18

when we should use this formula

Answer 19

Forget this formula.. I will tell you the method..

Answer 20

Do you know this formula:

\[A = (P+ \frac{PRT}{100})\]

Answer 21

This comes from :

A = P + SI

\[A = P + \frac{PRT}{100}\]

Right??

Answer 22

dont know

Answer 23

right

Answer 24

then

Answer 25

\[A_1 = P + \frac{6PT}{100}\]

Answer 26

So:

\[400 = P + \frac{6PT}{100} \\250 = P+ \frac{2PT}{100} \\Subtracting \\150 = \frac{4PT}{100} \\PT = 3750\]

Answer 27

Just check the calculation if I am doing right or not.. You must be having calculator or your genius mind with you.. :P

Answer 28

Now, can you find SI for any one of the given interest??

Answer 29

yes

Answer 30

\[SI_2 = \frac{PRT}{100 }\implies SI_2 = \frac{2 \times 3750}{100} \implies SI_2 = 75\]

Answer 31

a=p+225

Answer 32

I found it for second interest ie 2%.. You can also find it for 6%, it is your wish.

Amount = P + 75

Answer 33

It is for second interest rate, when you will do for 1st, you will get the same answer, don't worry about that..

So:

\[250 = P + 75 \implies P = 175\]

Answer 34

175+75=250

Answer 35

Suppose you find SI for 6%, then you will get :

SI = 225..

And A = P + 225:

P = 175 again.. It is for 6% case..

Answer 36

so amount 175 ahh

Answer 37

can you find time now??

Answer 38

Here is a shortcut, but you will not follow, just learn the method of doing it, but I am giving it to you.. :)

Answer 39

how?

Answer 40

I will write here, and you can do your work, it will take time to write.. :)

Answer 41

okay

Answer 42

u there

Answer 43

\(\text{If a certaiin sum P in a certain time, amounts to} \; A_1, \text{at the rate of} \; R_1 \%\), \(\text{and the same sum amounts to} \; A_2, \text{at the rate of} \; R_2 \%\), \(\text{then}\)

\[P = \frac{A_2 R_1 - A_1R_2}{R_1 - R_2}\]
\[T = (\frac{A_2 - A_1}{A_2R_1 - A_1R_2}) \times 100\]

Answer 44

okay thank you so much

Answer 45

Only to these type of problems, this formula will apply but I suggest you to learn the method, these formulas are just derived by letting 6% as R_1 and 400 as A_1, so they have become general formulae.. :) Keep it up..