Answer
Verified
405.3k+ views
Hint: We first assume the rate of interest for the principal amount has been under interest. We use the theorem of $a=\dfrac{pnr}{100}$ to relate the principal and the interest. We find the multiplied values of the variable from the first condition. We use that to find a solution to the problem.
Complete step-by-step solution
Rajan gave two people money of different value for 3 years at a certain rate of interest. For both cases, the rate of interest and time is the same.
Let’s assume the rate is r% annually. We term the time as n. So, $n=3$.
The amount of money for Rakesh and Mukesh is 1200 and 1000 respectively.
He got back Rs. 50 more from Rakesh than from Mukesh.
We have to calculate the interesting part.
We know that if the principal amount is p and the amount of interest is a, then the formula of finding the interest is defined by ${{a}_{i}}=\dfrac{pnr}{100}$.
For our given problem Rajan gave Rakesh 1200 rupees at a rate of r for 3 years.
We put the values $p=1200,n=3$ in the equation ${{a}_{1}}=\dfrac{pnr}{100}$. ${{a}_{1}}$ is the interest for Rakesh.
We get ${{a}_{1}}=\dfrac{1200\times 3\times r}{100}=36r$.
Rajan gave Mukesh 1000 rupees at a rate of r for 3 years.
We put the values $p=1000,n=3$ in the equation ${{a}_{2}}=\dfrac{pnr}{100}$. ${{a}_{2}}$ is the interest for Rakesh.
We get ${{a}_{2}}=\dfrac{1000\times 3\times r}{100}=30r$.
The difference of those two terms is $36r-30r=6r$ which is equal to 50.
Solving the equation, we get $6r=50\Rightarrow r=\dfrac{50}{6}=8\dfrac{1}{3}$.
The rating percentage is $8\dfrac{1}{3}$%. The correct option is A.
Note: We need to use simple interest if otherwise mentioned. In this problem, the principal was responsible for the change of interest value as the time span and the rate both were constant. In case of compound interest, the formula for interest would have been $a=p{{\left( 1+\dfrac{r}{100} \right)}^{n}}-p$.
Complete step-by-step solution
Rajan gave two people money of different value for 3 years at a certain rate of interest. For both cases, the rate of interest and time is the same.
Let’s assume the rate is r% annually. We term the time as n. So, $n=3$.
The amount of money for Rakesh and Mukesh is 1200 and 1000 respectively.
He got back Rs. 50 more from Rakesh than from Mukesh.
We have to calculate the interesting part.
We know that if the principal amount is p and the amount of interest is a, then the formula of finding the interest is defined by ${{a}_{i}}=\dfrac{pnr}{100}$.
For our given problem Rajan gave Rakesh 1200 rupees at a rate of r for 3 years.
We put the values $p=1200,n=3$ in the equation ${{a}_{1}}=\dfrac{pnr}{100}$. ${{a}_{1}}$ is the interest for Rakesh.
We get ${{a}_{1}}=\dfrac{1200\times 3\times r}{100}=36r$.
Rajan gave Mukesh 1000 rupees at a rate of r for 3 years.
We put the values $p=1000,n=3$ in the equation ${{a}_{2}}=\dfrac{pnr}{100}$. ${{a}_{2}}$ is the interest for Rakesh.
We get ${{a}_{2}}=\dfrac{1000\times 3\times r}{100}=30r$.
The difference of those two terms is $36r-30r=6r$ which is equal to 50.
Solving the equation, we get $6r=50\Rightarrow r=\dfrac{50}{6}=8\dfrac{1}{3}$.
The rating percentage is $8\dfrac{1}{3}$%. The correct option is A.
Note: We need to use simple interest if otherwise mentioned. In this problem, the principal was responsible for the change of interest value as the time span and the rate both were constant. In case of compound interest, the formula for interest would have been $a=p{{\left( 1+\dfrac{r}{100} \right)}^{n}}-p$.
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