Given:
Sum of money becomes 6 times of itself in 15 years
Formula used:
(i) SI = PRT/100
Where, P = principal
R = rate
T = time
(ii) A = SI + P
Where, A = Amount
SI = simple interest
Calculation:
Let the principal be P.
For 15 years,
SI = (P × R × 15)/100
⇒ 15PR/100
A = SI + P
⇒ 6P = 15PR/100 + P
⇒ 5P = 15PR/100
⇒ R = 500/15
⇒ R = 100/3 ≈ 33.33%
∴ The rate of interest is 33.33%.
Let Principal be P
So, Amount = 6P
And, Interest = 6P – P
⇒ 5P
Now, (P × R × 15)/100 = 5P
⇒ 3R/100 = 1
⇒ 3R = 100
⇒ R = 100/3 = 33.33%
∴ The rate of interest is 33.33%.
A sum of money at simple interest becomes four times in 24 years. What is the rate of interest per annum?
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Suggest Corrections4A sum of money becomes 4 / 3 of itself in 6 years at a certain rate of simple interest find the rate of interest.
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Suggest Corrections11$$\eqalign{ & {1^{{\text{st}}}}\,{\text{Method}}: \cr & {\text{Let rate is }}R\% \cr & {\text{Now}}, \cr & P = 100, \cr & A = 400, \cr & I = 400 - 100 = 300, \cr & {\text{Time}},\,T = 10\,{\text{years}} \cr & I = \frac{{PTR}}{{100}} \cr & {\text{Or}},R = \frac{{ {100 \times I} }}{{PT}} \cr & {\text{Or}},R = \frac{{ {100 \times 300} }}{{ {100 \times 10} }} \cr & {\text{Hence}},{\kern 1pt} R = 30\% \cr} $$
2nd Method :
Here, the sum become 4 times that means 100, become 400. Rate of such question is given by $$R = \frac{{{\text{interest}}}}{{{\text{time}}}} = \frac{{300}}{{10}} = 30\% $$3rd Method :
Here, 300% of rise in the sum so$$\eqalign{ & 100 - - - 300\% \uparrow - - - {\kern 1pt} 400; \cr & R = {\frac{{{\text{total}}\,{\text{percentage rise}}}}{{{\text{given time}}}}} \cr & \,\,\,\,\,\,\,\, = \frac{{300\% }}{{10}} \cr & \,\,\,\,\,\,\,\, = 30\% \cr} $$
The rate at which a sum becomes 4 times of itself in 16 years at simple interest is.....
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Solution
The correct option is C
300/16%
P×R×T100 = I
4P = P+I
I = 3P
3P = P×R×16100
R = 30016
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A sum of money becomes 4 / 3 of itself in 6 years at a certain rate of simple interest find the rate of interest.
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Solution
Let the rate of interest is r and sum of money be x
it becomes
4x3 in 6 yrs
So, SI in 6 yrs
=4x3−x=x3
As we know that SI
=ptr100, where p=x, t=6.
or
x3=x×6×r100
or
r=509
∴r=5.56% (approx)
So, rate of interest 5.56%
Suggest Corrections
11
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A sum of money becomes 6 times of itself in 8 years. Find the rate of Simple Interest.