Question

please tell me who are intelligent in all subjects please answer this​

Answer 1

Step-by-step explanation:

Given :-

A person deposited some money at 10% per annum at Compound interest after 2 years he withdraw RS. 2050 and remaining is deposited in Bank for third year.The ratio of 3rd year and 2nd years Compound interests is 8:21.

To find :-

Find the initial deposited money ?

Solution :-

Let the initial deposited money be Rs.X

Rate of interest = 10%

Time of the period = 2 years

We know that

Amount = P[1+(R/100)]^n

=> Amount after 2 years

=> X[1+(10/100)]²

=> X[ 1+(1/10)]²

=> X [(10+1)/10]²

=> X(11/10)²

=> X(11×11)/(10×10)

=> X(121/100)

=> 121X/100

Amount after 2 years = Rs. 121X/100

We know that

Amount = Principle + Interest

Compound Interest = Amount - Principle

=> CI = (121X/100)-X

=> CI = (121X-100X)/100

=> CI = 21X/100

Compound Interest for 2 years = Rs.21X/100---(1)

Now after 2 years ,

Money withdrawn by him = Rs. 2050

Remaining Money

= (121X/100 )-2050

= (121X-205000)/100

Remaining Amount = Rs. (121X-205000)/100

It will become Principle for the third year

P = Rs. (121X-205000)/100

He deposited it again at same rate of interest for third year

=> Amount = P[1+(R/100)]¹

=> A = P[1+(R/100)]

=> A = [(121X-205000)/100][1+(10/100)]

=> A = [(121X-205000)/100][(11/10)]

=> A =[(121X-205000)×11]/1000

Compound Interest = A - P

=> [(121X-205000)×11]/1000 -(121X-205000)/100

=> [(121X-205000)×11]-[(121X-205000)×10]/1000

=> (121X-205000)(11-10)/1000

=> (121X-205000)/1000

CI for third year = Rs. (121X-205000)/1000----(2)

Ratio of the Compound interest for third year and 2 years

=>(121X-205000)/1000: 21X/100

=> (121X-205000)/10:21X

Given that

The ratio of 3rd year and 2nd years Compound interests is 8:21.

=> (121X-205000)/10:21X = 8:21

=> (121X-205000)/10:21X = 8:21

=> (121X-205000)/10(21X) = 8/21

=> (121X-205000)/10X = 8

=> 121X-205000 = 8×10X

=> 121X -205000 = 80X

=> 121X-80X = 205000

=> 41X = 205000

=> X = 205000/41

=> X = 5000

Therefore the value of X = Rs. 5000

Answer:-

The initial money deposited by the man is

Rs. 5000

Used formulae:-

• Amount = P[1+(R/100)]^n

• Amount = Principle + Interest

Where, A = Amount

• P = Principle

• n = Number of times the compound interest calculated

• R = Rate of interest