An intercity cab service has a lumpsum fixed charges of Rs. 800 upto certain kilometer. Beyond that

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19 Aug 2022 Arithmetic

An intercity cab service has a lumpsum fixed charges of Rs. 800 upto certain kilometer. Beyond that the charges are per kilometer. When two passengers separately travelled total 450 km, they were charged Rs. 2600 and Rs. 2000 respectively. If a single passenger had travelled all 450 km, he would have been charged Rs. 5000. How many kilometers are allowed for first Rs. 800 ?

OPtion

1) 90
2) 80
3) 150
4) 120
5) 200
6) 125
7) 100
8) 180
9) 225
10) None of these

Solution

When two passengers together travells 450 km, let 1st passenger travells 'x' km and 2nd travells (450-x) km.
Let Rs. 800 are charges upto 'a' km and charge per km beyond 'a' km is Rs. 'r'
Charges of 1st passenger = 800 + (x-a)*r = 2600 ⇒ xr - ar = 1800 ---(i)
Charges of 2nd passenger = 800 + (450-x-a)*r = 2000 ⇒ 450r - xr - ar = 1200 ---(ii)
Charges when single passenger travells 450 km = 800 + (450-a)*r = 5000 ⇒ 450r - ar = 4200 ---(iii)
Adding eqn (i) & (ii), we get 450r - 2ar = 3000 ⇒ 225r - ar = 1500 ---(iv)
Subtracting eqn (iv) from (iii), we get r=12
And substituting value of r=12, in eqn (iv), we get 225(12) - a(12) = 1500
2700 - 12a = 1500
a = 100
Correct Option 7)

Correct Option: 7 Best Solution (0)