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A sum of money amount to Rs 6200 in 2 years and Rs 7400 in 3 years. The principal and rate of interest are ?
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A sum of money amount to Rs 6200 in 2 years and Rs 7400 in 3 years. Th...
Given information:
- Amount after 2 years = Rs 6200
- Amount after 3 years = Rs 7400

Calculating the principal:
To find the principal, we need to subtract the interest from the total amount.

Let's assume the principal amount is P and the rate of interest is R.

After 2 years, the amount is given by:
Amount = Principal + Interest
Rs 6200 = P + (P * R * 2/100)

After 3 years, the amount is given by:
Amount = Principal + Interest
Rs 7400 = P + (P * R * 3/100)

Solving the equations:
To solve these equations, we can use the method of substitution.

From the first equation:
Rs 6200 = P + (P * R * 2/100)
Rs 6200 = P + (2PR/100)
Rs 6200 = P(1 + 2R/100) --> Equation 1

From the second equation:
Rs 7400 = P + (P * R * 3/100)
Rs 7400 = P + (3PR/100)
Rs 7400 = P(1 + 3R/100) --> Equation 2

Now, we have two equations with two variables (P and R).

Calculating the rate of interest:
To solve for R, we can divide Equation 2 by Equation 1.

(Rs 7400)/(Rs 6200) = (P(1 + 3R/100))/(P(1 + 2R/100))
7400/6200 = (1 + 3R/100)/(1 + 2R/100)

Simplifying the equation, we get:
37/31 = (1 + 3R/100)/(1 + 2R/100)

Cross-multiplying, we get:
37(1 + 2R/100) = 31(1 + 3R/100)

Solving this equation will give us the value of R.

Calculating the principal:
Once we have the value of R, we can substitute it back into Equation 1 to find the principal amount.

Rs 6200 = P(1 + 2R/100)

Solving this equation will give us the value of P.

Therefore, the principal and rate of interest can be calculated using the above steps.
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A sum of money amount to Rs 6200 in 2 years and Rs 7400 in 3 years. The principal and rate of interest are ?
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