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The Simple Interest on a certain sum of money for two years is Rs. 40 and the CI on same sum at same rate for same time is Rs. 40.50. Find the sum.
- a)Rs. 1600
- b)Rs. 800
- c)Rs. 600
- d)None
- e)All of the above
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The Simple Interest on a certain sum of money for two years is Rs. 40 ...
SI for 2 years=40
THUS,SI for 1 year=40/2=20
As for the first year CI and SI are always same so,
CI for first year=20
give that CI for 2 years is 40.5;
So CI for second year =40.5-20=20.5
Difference in CI for two successive years=20.5-20=0.5
so;
0.5 is the interest for one year on the interest of first year,that is,on rupees 20;
thus,
rate=(100*I)/(P*T)
=(100*0.5)/(20*1)
=2.5 percent
therefore; the rate is 2.5 % per annum
P = (100*I)/(R*T)
= (100*40)/(2.5*2)
= 4000/5
= 800 , i.e. , (b)
THUS,SI for 1 year=40/2=20
As for the first year CI and SI are always same so,
CI for first year=20
give that CI for 2 years is 40.5;
So CI for second year =40.5-20=20.5
Difference in CI for two successive years=20.5-20=0.5
so;
0.5 is the interest for one year on the interest of first year,that is,on rupees 20;
thus,
rate=(100*I)/(P*T)
=(100*0.5)/(20*1)
=2.5 percent
therefore; the rate is 2.5 % per annum
P = (100*I)/(R*T)
= (100*40)/(2.5*2)
= 4000/5
= 800 , i.e. , (b)
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Community Answer
The Simple Interest on a certain sum of money for two years is Rs. 40 ...
Given, Simple Interest (SI) for 2 years = Rs. 40
Compound Interest (CI) for 2 years = Rs. 40.50
Let the principal be x and rate be r.
As we know, SI = (P * R * T)/100
Substituting the given values, we get, 40 = (x * r * 2)/100
=> 2rx = 400
Similarly, we know, CI = P[(1 + (R/100))^T - 1]
Substituting the given values, we get, 40.50 = x[(1 + r/100)^2 - 1]
=> x[(1 + r/100)^2] = 40.50 + x
Now, we can substitute 2rx = 400 in the second equation and simplify it to get x = Rs. 800.
Therefore, the sum of money is Rs. 800 (Option B).
Compound Interest (CI) for 2 years = Rs. 40.50
Let the principal be x and rate be r.
As we know, SI = (P * R * T)/100
Substituting the given values, we get, 40 = (x * r * 2)/100
=> 2rx = 400
Similarly, we know, CI = P[(1 + (R/100))^T - 1]
Substituting the given values, we get, 40.50 = x[(1 + r/100)^2 - 1]
=> x[(1 + r/100)^2] = 40.50 + x
Now, we can substitute 2rx = 400 in the second equation and simplify it to get x = Rs. 800.
Therefore, the sum of money is Rs. 800 (Option B).
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The Simple Interest on a certain sum of money for two years is Rs. 40 and the CI on same sum at same rate for same time is Rs. 40.50. Find the sum.a)Rs. 1600b)Rs. 800c)Rs. 600d)Nonee)All of the aboveCorrect answer is option 'B'. Can you explain this answer?
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