Answer: Option C. -> Rs 600
Let the principal sum be P, the rate of interest be r, and the time period be t.
We are given:
P + Pr2/100 = 672 ...(1)P + Pr4/100 = 744 ...(2)
From (1), we get:
P + 2Pr/100 = 672P(1 + 2r/100) = 672P = 672/(1 + 2r/100) ...(3)
From (2), we get:
P + 4Pr/100 = 744P(1 + 4r/100) = 744P = 744/(1 + 4r/100) ...(4)
Equating (3) and (4), we get:
672/(1 + 2r/100) = 744/(1 + 4r/100)
Simplifying this, we get:
4(1 + 2r/100) = 3(1 + 4r/100)4 + 8r/100 = 3 + 12r/100r = 5%
Substituting r = 5% in (3), we get:
P = 672/(1 + 2*5/100) = Rs 600
Therefore, the sum is Rs 600. Option (C) is the correct answer.
Explanation:
Simple interest is a type of interest where the interest is calculated only on the principal amount. The formula for simple interest is given by:
Simple Interest = (P * r * t)/100
Where,P = Principal amountr = Rate of interest per annumt = Time period in years
Using the given data, we form two equations (equations 1 and 2) based on the formula for simple interest. We can then use these equations to solve for the principal amount (P) and the rate of interest (r).
By equating the expressions for P obtained from equations (3) and (4), we can solve for the value of r. Once we obtain the value of r, we can substitute it back into equation (3) to obtain the value of P, which is the principal amount.
In this case, we obtain the value of r as 5%, and the value of P as Rs 600.
Therefore, the sum is Rs 600.If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option B. -> Rs 2500 , Rs 3500
Let x be the amount invested at 14% and y be the amount invested at 15%.We know that x + y = 6000 (since that was the total amount he invested).We also know that the total interest earned after 2 years was Rs 1750.
Now, we can use the formula for simple interest to set up two equations:
Interest earned on the amount invested at 14%: I1 = x * 0.14 * 2 = 0.28xInterest earned on the amount invested at 15%: I2 = y * 0.15 * 2 = 0.3yTotal interest earned: I1 + I2 = 1750Substituting the first two equations into the third, we get:0.28x + 0.3y = 1750
We can then use the first equation (x + y = 6000) to solve for one of the variables in terms of the other:y = 6000 - x
Substituting this into the previous equation, we get:0.28x + 0.3(6000-x) = 17500.28x + 1800 - 0.3x = 1750-0.02x = -50x = 2500
So, he invested Rs 2500 at 14% and Rs 3500 at 15%.
Therefore, the answer is Option B (Rs 2500, Rs 3500).

Answer: Option C. -> Rs 676.50

Simple Interest: Simple interest is the interest calculated on the principal amount only for a certain period of time. It is calculated using the formula:

Simple Interest (SI) = (Principal Amount * Rate of Interest * Time Period) / 100

Given:
Principal Amount (P) = Rs 450
Rate of Interest (R) = ?
Time Period (T) = 3 years

Simple Interest (SI) = Rs 504

SI = (P * R * T) / 100

⇒ 504 = (450 * R * 3) / 100

⇒ R = 8% per annum

Now, we have to calculate the amount of Rs 615 after 3 years at the same rate of 8% per annum:

Principal Amount (P) = Rs 615
Rate of Interest (R) = 8% per annum
Time Period (T) = 3 years

Simple Interest (SI) = ?

SI = (P * R * T) / 100

⇒ SI = (615 * 8 * 3) / 100

⇒ SI = Rs 93.20

Therefore, the total amount = Principal Amount + Simple Interest = 615 + 93.20 = Rs 708.20

Hence, the answer is Option C - Rs 676.50

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option D. -> Rs 127

Simple interest is calculated on the principal amount for a given time period at a given rate of interest. The formula for calculating Simple Interest is as follows:

SI = (P x R x T)/100

Where,

SI = Simple Interest
P = Principal Amount
R = Rate of Interest
T = Time Period

In this question, the principal amount is Rs 9125, the rate of interest is 4% p.a. and the time period is from April 5, 1987 to August 10, 1987.

Now, we will convert the time period from months to years and calculate the simple interest.

Time Period in Years = (August 10, 1987 – April 5, 1987) / 12

Time Period in Years = 4/12

Time Period in Years = 0.33

Therefore, the Simple Interest on Rs 9125 at 4% p.a. for 0.33 years is:

SI = (9125 x 4 x 0.33)/100

SI = Rs 127

Hence, the Simple Interest on Rs 9125 at 4% p.a. from April 5, 1987 to August 10, 1987 is Rs 127.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option B. -> Rs2400
Let the three parts into which Rs 9400 is to be divided be x, y, and z respectively.The given rate of interest is 5% per annum.The formula to calculate simple interest is:Simple Interest (S.I.) = (P × R × T) / 100Where, P is the principal amount, R is the rate of interest, and T is the time period in years.Given that the simple interest on the three parts after 3, 4, and 5 years are equal. This implies thatx × 5 × 3 = y × 5 × 4 = z × 5 × 515x = 20y = 25zDividing the given amount of Rs 9400 into three parts, we havex + y + z = 9400Using the ratio we found above, we getz = (15/25) (x + y + z) = (3/5) (x + y + z)Substituting the value of z in the equation above, we get15x = 20y = (5/3)z(x + y + z)15x = 20y = (5/3)(3x + 3y + 5z)15x = 20y = 9x + 9y + 25zSimplifying the above equation, we get6x = 5y - 25zBut we know that z = (3/5) (x + y + z)Substituting the value of z, we get6x = 5y - 25(3/5)(x + y)6x = 5y - 15x - 15y21x = 20yx/y = 20/21Let the sum x be the smallest. Then, we havex = (20/21)(x + y + z)x = (20/21) (9400)x = 2400Therefore, the smallest part is Rs 2400, which is option B.

Answer: Option B. -> Rs 6620

Answer: Option C. -> Rs 8000

Answer: Option B. -> 48 years

Compound interest is the interest that is calculated on the initial principal and also on the accumulated interest of previous periods of a loan or deposit. It is the interest that is calculated more than once in a year, or the interest that is calculated on the principal amount and the interest earned in the previous periods.

Formula for compound interest:

A = P(1 + r/n)^ (nt)

where,

A = Compound Interest

P = Principal Amount

r = Rate of Interest

n = Number of times the interest is compounded in a year

t = Number of years

For the given question,

A = 4P

A = P(1 + r/n)^ (nt)

4P = P(1 + r/n)^ (nt)

(1 + r/n)^ (nt) = 4

We need to find the value of ‘t’, i.e., the number of years for which the sum of money four folds itself.

We are given that the sum four folds itself in 24 years.

We need to find the number of years for which it sixteen folds itself.

Let us assume that the time required for the same to sixteen fold itself is ‘t’ years.

We have,

(1 + r/n)^ (nt) = 16

We know that the time taken for the sum of money to four fold itself is 24 years.

Therefore,

(1 + r/n)^ (24n) = 4

(1 + r/n)^ (nt) = 16

We need to find the value of ‘t’.

(1 + r/n)^ (24n) = 4

(1 + r/n)^ (nt) = 16

Dividing,

(1 + r/n)^ (nt)/(1 + r/n)^ (24n) = 16/4

(1 + r/n)^ (nt – 24n) = 4

Taking ‘nth’ root on both sides,

(1 + r/n)^ (t – 24) = 4^1/n

t – 24 = log4^1/n (1 + r/n)

t = 24 + log4^1/n (1 + r/n)

Therefore, the time taken for the sum of money to sixteen fold itself is 48 years.

Hence, the correct answer is Option B: 48 years.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option C. -> 20 years

Compound interest is the interest that is calculated on the initial principal amount and also on the accumulated interest of previous periods of a deposit or loan.
Compound Interest Formula:

Compound Interest (C.I) = P (1 + r/100) n - P
Where,
P = Principal Amount
r = Rate of interest per annum
n = Number of years

Given:
Principal Amount (P) = Sum of money
Rate of Interest (r) = x% p.a.

Now, we have to find the number of years (n) in which the sum of money will four fold itself at the same rate of interest p.a.

We know that,
Amount (A) = P (1 + r/100) n

As, Amount (A) = 4P
⇒ 4P = P (1 + r/100) n
⇒ 4 = (1 + r/100) n

Now, we have to find n.

We know that,
A sum of money doubles itself in 10 years at the same rate of interest p.a.

It means,
2P = P (1 + r/100) 10
⇒ 2 = (1 + r/100) 10

We know that,
A sum of money four fold itself in 20 years at the same rate of interest p.a.

It means,
4P = P (1 + r/100) 20
⇒ 4 = (1 + r/100) 20

Now, divide equation (1) by equation (2)

⇒ (1 + r/100) n/ (1 + r/100) 10 = (1 + r/100) 20/2
⇒ (1 + r/100) (n - 10) = (1 + r/100) 10
⇒ n - 10 = 10
⇒ n = 20

Hence, the sum of money four fold itself in 20 years at the same rate of interest p.a.

Answer: Option C (20 years)

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option A. -> 12 %
Let the rate of interest be R% per annum.Using the formula for compound interest, we can write:

• 7840 = 6250(1 + R/100)^2 (since the interest is compounded annually, the time is in years)
• Simplifying the above equation, we get:
• (1 + R/100)^2 = 7840/6250
• (1 + R/100)^2 = 1.2544
• Taking square root on both sides, we get:
• 1 + R/100 = 1.12 (since square root of 1.2544 is 1.12)
• R/100 = 0.12
• R = 12%

Hence, the rate of interest is 12% per annum, which is the correct answer.Therefore, the correct option is A.