Correct Answer – Option 2 : Rs. 3037500

Given:

Present fare per person = Rs. 1000, total fare charged by the train = Rs. 2500000,

The fare of a royal train between to stations increases at the rate of 25% per month at simple interest,

The number of passenger decreases at the rate of 10% per annum compounded monthly

Formula used:

S.I = P × R × T/100

\({\rm{A}} = {\rm{P\;}}{\left( {1 – {\rm{\;}}\frac{{\rm{r}}}{{100}}} \right)^2},\;where\;A = final\;amount\;and\;p = initial\;amount\;of\;water\)

Calculation:

Present number of passenger in the train = 2500000/1000 = 2500

Fare per person in the 2nd month = 1000 + 1000 × 25 × 2/100 = Rs. 1500

Number of passenger in the 2nd month = 2500 (1 – 10/100)² = 2025

So, the total amount earned by the train authority = 2025 × 1500 = Rs. 3037500.

Correct Answer – Option 2 : Rs. 10800

Given:

C.I. – S.I. = Rs. 27

R = 5%

N = 2 years

Formula used:

In case of compound interest

A = P × {1 + (R / 100)}^N

Where P = Principal amount, R = Rate of interest in %, N = Number of years, A = Amount

In case of simple interest

I = PRN / 100

Where P = Principal amount, R = Rate of interest in %, N = Number of years, I = Interest earned

A = P + I

Calculation:

Here, C.I. – S.I. = 27

Also, C.I. = P × {1 + (R / 100)}^N – P

And S.I = PRN/100

Accordingly,

⇒ P × {1 + (R / 100)}N – P – (PRN / 100) = 27

⇒ P{(1 + R/100)^N – 1 – (RN/100)} = 27

⇒ P{(1 + 5/100)² – 1 – (5 × 2)/100} = 27

⇒ P × {441/400 – 1 – 1/10} = 27

⇒ P × (1/400) = 27

⇒ P = 27 × 400

⇒ P = 10800

∴ Principal amount is Rs. 10800.

Correct Answer – Option 4 : Rs. 5082

Given:

A = Rs. 6048 (after 2 years)

A = Rs. 7257.6 (After 3 years)

Formula used:

A = P × {1 + (R/100)}^N

Where, P = Principal, R = Rate of interest, N = Number of years

Calculation:

Let Amount after 3 years and 2 years be A3/A2 respectively.

Here, A₃/A₂ = 7257.6/6048

⇒ 7257.6/6048 = 1.20

A3/A2 = [P{1 + (R/100)}3]/[P{1 + (R/100)}2]

⇒ 1.20 = {1 + (R/100)}

⇒ 0.20 = R/100

⇒ R = 20%

Now, calculating P,

⇒ 6048 = P × {1 + (20/100)}²

⇒ 6048 = (P × 6 × 6)/(5 × 5)

⇒ P = Rs. 4200

∵ R decreased to 10%,

⇒ New rate of interest is (20 – 10) = 10%

A = 4200 × {1 + (10/100)}²

⇒ A = (4200 × 11 × 11)/(10 × 10)

⇒ A = 5082

∴ He will receive Rs. 5082 at the end of two years if the rate of percentage decreases by 10%.

Correct Answer – Option 1 : Rs. 128,000

Given:

A certain sum of money becomes 7 times of itself in 18 years if invested at the simple interest.

Formula used:

Amount = P[1 + (r/100)]^T

Calculation:

A sum of money becomes 7 times of itself in 18 years

Let the sum be x

The amount after 18 years will be 7x.

Interest = 7x – x = 6x

S I = (p × r × t)/100

6x = (x × r × 18)/100

r = 100/3%

If the rate of interest divided by 100 is applied on a sum of Rs. 54000 for three years under compound interest,

R = 100/3%

According to the question,

Amount = 54000 (1 + 1/3)³

⇒ 23000 × 4 × 4 × 4

⇒ Rs. 128000

∴ The amount after 4 years is Rs. 128,000