Ci and si of a certain sum at certain rate of interest are 720 and 600 respectively what is the principal for two years for thesr interests
Answers
Step-by-step explanation:
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If the C.I. is Rs. 720 and the S.I. is Rs. 600 at certain sum and interest then the principal for two years for their interests is Rs. 750.
Step-by-step explanation:
Required Formula:
- S.I. = [PRT]/100
- C.I. = P [(1+R/100)ⁿ - 1]
It is given that,
Compound Interest, C.I. = Rs. 720
Simple Interest, S.I. = Rs. 600
Time period, T or n = 2 years
Let the sum of money for both the cases be Rs. “P” and the rate of interest be "R%"
Now,
Substituting the given values in the first formula of simple interest, we get
600 = [PR * 2]/100
⇒ PR = [600 * 100]/2
⇒ P = 30000/R …… (i)
Again substituting the value in the second formula of compound interest, we get
720 = P [(1+R/100)² - 1]
Substituting the value of P from (i)
⇒ 720 = [(30000/R) * (1+R/100)²] – [30000/R]
⇒ 720 = [(30000/10000R) * (100+R)²] – 30000/R
⇒ 720R = [3(10000 + 200R + R²)] – 30000
⇒ 720R = 30000 + 600R + 3R² – 30000
⇒ 720R = 600R + 3R²
⇒3R² = 120R
⇒ 3R = 120
⇒ R = 40% ….. (ii)
Thus, from (i) & (ii), we get
The principal amount for 2 years of interest as,
= 30000/R
= 30000/40
= Rs. 750
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