12. A sum of 6000 amounts to ₹ 6900 in 3 years. What will it amount to if the rate of interest is increased by 2%?
Answers
Answer:
First case :-
Principal amount = Rs. 6000
Amount = Rs. 6900
Time = 3 years
Second case :-
Rate of interest increased by 2 %
Required to find :-
Rate of interest ( in the 1st case )
Amount (2nd case )
Formulae used :-
\large{\leadsto{\boxed{\rm{ Simple \; Interest = \dfrac{PTR }{100}}}}}⇝
SimpleInterest=
100
PTR
\large{\leadsto{\boxed{\rm{ Amount = Principal + Interest }}}}⇝
Amount=Principal+Interest
Solution :-
Consider the 1st case ;
Given that :-
Principal amount = Rs. 6000
Amount = Rs. 6900
Time = 3 years
He asked us to find the rate of interest .
In order to find the rate of interest we should find the interest
As we know that,
Amount = principal + Interest
So,
Interest = Amount - principal
Substitute the required values
Interest = 6900 - 6000
Interest = Rs. 900
Hence
Using the formula ,
\large{\leadsto{\boxed{\rm{ Simple \; Interest = \dfrac{PTR }{100}}}}}⇝
SimpleInterest=
100
PTR
Here,
P = principal
T = Time
R = Rate of interest
However,
Let the rate of interest be " x "
Substitute the value
Here,
Simple Interest = Rs. 900
So,
\longrightarrow{\tt{900 = \dfrac{6000 \times 3 \times x }{100}}}⟶900=
100
6000×3×x
\longrightarrow{\tt{ 900 = 60 \times 3 \times x }}⟶900=60×3×x
\longrightarrow{\tt{900 = 180x }}⟶900=180x
Interchange the terms on both sides
\Rightarrow{\tt{ 180x = 900 }}⇒180x=900
\longrightarrow{\tt{ x = \dfrac{900}{180}}}⟶x=
180
900
\longrightarrow{\tt{ x = 5 \% }}⟶x=5%
Hence,
Rate of interest ( % ) = x = 5 %
So,
Now consider the 2nd case .
In this case we can use some values which is given in the First case should be used expect rate of interest , amount .
Because,
He mentioned that :-
If the rate of interest is increased by 2%
So,
The values are;
Principal = Rs. 6,000
Rate of interest = 5% + 2% = 7%
Time = 3 years
Using the formula ,
\large{\leadsto{\boxed{\rm{ Simple \; Interest = \dfrac{PTR }{100}}}}}⇝
SimpleInterest=
100
PTR
So,
\longrightarrow{\tt{ S.I. = \dfrac{ 6000 \times 3 \times 7}{100}}}⟶S.I.=
100
6000×3×7
\longrightarrow{\tt{ S.I. = 60 \times 3 \times 7 }}⟶S.I.=60×3×7
\longrightarrow{\tt{ S.I. = Rs. \; 1260}}⟶S.I.=Rs.1260
Hence,
Interest = Rs. 1260
Now ,
Using the formula in order to find the amount
\large{\leadsto{\boxed{\rm{ Amount = Principal + Interest }}}}⇝
Amount=Principal+Interest
So,
\rm{Amount = Rs. \; 6000 + Rs. \; 1260 }Amount=Rs.6000+Rs.1260
\rm{Amount = Rs. 7260 }Amount=Rs.7260
\large{\leadsto{\boxed{\tt{\therefore{Amount = Rs. \; 7260 }}}}}⇝
∴Amount=Rs.7260
Answer:
₹ (6,900 - 6,000) = 900 for 3 years is the S.I. ⟹ R = 5% p.a.
Step-by-step explanation:
hope it is help
