The fare of a royal train between two stations increases at the rate of 25% per month at simple interest and the number of passengers decreases at the rate of 10% per month compounded monthly. If the present fare per person and the total fare charged by the train are Rs. 1000 and Rs. 2500000 respectively, then find the total fare earned by the train authority in the 2nd month.
1. Rs. 3037000
2. Rs. 3037500
3. Rs. 3030000
4. Rs. 3000000
1. Rs. 3037000
2. Rs. 3037500
3. Rs. 3030000
4. Rs. 3000000
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.