Answer
Verified
414.6k+ views
Hint: In this question, we need to determine the principal sum of money that will amount to INR 2832 in the time period of 5 years with $ 9\dfrac{1}{2}\% $ as the rate of interest. For this, we will use the relation between the amount, principal amount, rate of interest and time period.
Complete step-by-step answer:
Here, the rate of interest has been given as in mixed fraction, so first, we will convert the mixed fraction to the proper fraction by following $ a\dfrac{b}{c} = \dfrac{{ac + b}}{c} $ .
Here, a=9, b=1 and c=2 so,
$
9\dfrac{1}{2} = \dfrac{{9 \times 2 + 1}}{2} \\
= \dfrac{{19}}{2}\% \\
$
Now, the product of the principal amount, rate of interest (in decimal equivalent) and the time period result in the interest on the amount that one will get after the specified time period. Mathematically, $ I = \dfrac{{prt}}{{100}} $ where, I is the interest gained, p is the principal amount, r is the rate of interest and t is the time period.
So, substitute $ r = \dfrac{{19}}{2}\% $ and t=5 years in the formula $ I = \dfrac{{prt}}{{100}} $ to determine the expression for the interest gained in terms of the principal amount.
$
\Rightarrow I = \dfrac{{prt}}{{100}} \\
= \dfrac{{p\left( {\dfrac{{19}}{2}} \right)5}}{{100}} \\
= \dfrac{{95p}}{{200}} \\
= \dfrac{{19p}}{{40}} \\
$
The amount is the summation of the principal amount and the interest gained on the principal amount.
According to the question, the amount $ (A = p + I) $ is INR 2832. So, substitute $ I = \dfrac{{19p}}{{40}} $ in the equation $ (A = p + I) $ to determine the principal amount.
$
\Rightarrow A = p + I \\
\Rightarrow 2832 = p + \dfrac{{19p}}{{40}} \\
\Rightarrow 2832 = \dfrac{{40p + 19p}}{{40}} \\
\Rightarrow 69p = 2832 \times 40 \\
\Rightarrow p = \dfrac{{2832 \times 40}}{{69}} \\
= 1641.7 \\
$
Hence, the INR 1641.7 sum of money amounts to INR 2832 in 5 years at $ 9\dfrac{1}{2}\% $ the rate of interest.
Note: Students should know how to convert mixed fraction to proper fraction. Moreover, whenever the question is not indicating the type of interest (simple or compound) then, we should by default always consider for the simple interest only.
Complete step-by-step answer:
Here, the rate of interest has been given as in mixed fraction, so first, we will convert the mixed fraction to the proper fraction by following $ a\dfrac{b}{c} = \dfrac{{ac + b}}{c} $ .
Here, a=9, b=1 and c=2 so,
$
9\dfrac{1}{2} = \dfrac{{9 \times 2 + 1}}{2} \\
= \dfrac{{19}}{2}\% \\
$
Now, the product of the principal amount, rate of interest (in decimal equivalent) and the time period result in the interest on the amount that one will get after the specified time period. Mathematically, $ I = \dfrac{{prt}}{{100}} $ where, I is the interest gained, p is the principal amount, r is the rate of interest and t is the time period.
So, substitute $ r = \dfrac{{19}}{2}\% $ and t=5 years in the formula $ I = \dfrac{{prt}}{{100}} $ to determine the expression for the interest gained in terms of the principal amount.
$
\Rightarrow I = \dfrac{{prt}}{{100}} \\
= \dfrac{{p\left( {\dfrac{{19}}{2}} \right)5}}{{100}} \\
= \dfrac{{95p}}{{200}} \\
= \dfrac{{19p}}{{40}} \\
$
The amount is the summation of the principal amount and the interest gained on the principal amount.
According to the question, the amount $ (A = p + I) $ is INR 2832. So, substitute $ I = \dfrac{{19p}}{{40}} $ in the equation $ (A = p + I) $ to determine the principal amount.
$
\Rightarrow A = p + I \\
\Rightarrow 2832 = p + \dfrac{{19p}}{{40}} \\
\Rightarrow 2832 = \dfrac{{40p + 19p}}{{40}} \\
\Rightarrow 69p = 2832 \times 40 \\
\Rightarrow p = \dfrac{{2832 \times 40}}{{69}} \\
= 1641.7 \\
$
Hence, the INR 1641.7 sum of money amounts to INR 2832 in 5 years at $ 9\dfrac{1}{2}\% $ the rate of interest.
Note: Students should know how to convert mixed fraction to proper fraction. Moreover, whenever the question is not indicating the type of interest (simple or compound) then, we should by default always consider for the simple interest only.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Why Are Noble Gases NonReactive class 11 chemistry CBSE
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
At which age domestication of animals started A Neolithic class 11 social science CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Write a letter to the principal requesting him to grant class 10 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE