Question

2. A certain sum of money becomes
*2250 at the end of 2 yr and
becomes 2625 at the end of 5 yr.
If the person receives only simple
interest, then the rate of interest is in short trick
​

Answer 1

Answer:

don't know the answer

Answer 2

Step-by-step explanation:

Given:-

A certain sum of money becomes Rs.2250 at the end of 2 years and becomes Rs. 2625 at the end of 5 years .

To find:-

If the person receives only simple interest, then Find the rate of interest ?

Solution:-

Short cut:-

Let the rate of interest be R %

First amount = Rs .2520 in 2 years

A1 = Rs. 2520

t1 = 2 years

Second amount = Rs. 2625 in 5 years

A2 = Rs. 2625

t2 = 5 years

If a sum amounts to Rs. A1 in t1 years and Rs. A2 in t2 years at simple interest then Rate of interest per annum is [100(A2-A1)] / (A1t2-A2t1)

=>R = [100(2625-2250)] / [(2250×5)-(2625×2)]

=>R = 100(375)/(11250-5250)

= R = 37500/6000

=>R=375/60

=>R= 75/12

=>R = 6.25%

Rate of interest = 6.25%

General method:-

Let the sum be Rs. P

Let the rate of interest be R%

Amount (A)=Rs.2250

Time (T)=2 years

we know that

I = PTR/100

A = P+I

=>A = P+(PTR/100)

=>P+(P×2×R/100)=2250

=>P+(2PR/100)=2250

=>(100P+2PR)/100 = 2250

=>(50P+PR)/50 = 2250

=>50P+PR = 2250×50

=>50P +PR =112500--------(1)

Sum =Rs. P

Time (T)=5 years

Amount (A)=Rs. 2625

A = P+(PTR/100)

=>P+(P×5×R)/100=2625

=>P+(5PR)/100=2625

=>P+(PR/20)=2625

=>(20P+PR)/20 = 2625

=>20P+PR = 2625×20

=>20P+PR = 52500--------(2)

On subtracting (2) from (1) then

.

50P +PR =112500

20P+PR = 52500

(-)

_______________

30P +0 = 60000

________________

=>30 P = 60000

=>P = 60000/30

=>P = Rs. 2000

The sum is Rs. 2000

Now on Substituting the value of P in (2) then

20(2000)+2000R = 52500

=>40000+2000R = 52500

=>2000R = 52500-40000

=>2000R = 12500

=>R = 12500/2000

=>R = 125/20

=>R = 6.25%

Rate of interest = 6.25%

.

Answer:-

The rate of interest for the given problem is 6.25%

Used formulae:-

• Simple Interest (I)=PTR/100

• Amount = Principle+ Interest

• If a sum amounts to Rs. A1 in t1 years and Rs. A2 in t2 years at simple interest then Rate of interest per annum is
• [100(A2-A1) ]/ (A1t2-A2t1)