175 views

0 votes

The local office of the $\text{AA-CAB}$ company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters $(\text{P1}$ and $\text{P5})$ as given below:

$\text{P1}$: timely arrival

$\text{P2}$: behaviour

$\text{P3}$: comfortable ride

$\text{P4}$: driver’s familiarity with the route

$\text{P5}$: value for money

Based on feedback from the customers, the office assigns a rating from $1$ to $5$ in each of these parameters. Each rating is an integer from a low value of $1$ to a high value of $5$. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts$-$a fixed payment and final rating$-$based bonus. If a driver gets a rating of $1$ in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters.

The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:

$\text{P1}$ | $\text{P2}$ | $\text{P3}$ | $\text{P4}$ | $\text{P5}$ | Fixed payment | Bonus | |

Arun | $4$ | Rs.$1000$ | Rs.$250\times$Final Rating | ||||

Barun | $3$ | Rs.$1200$ | Rs.$200\times$Final Rating | ||||

Chandan | $2$ | Rs.$1400$ | Rs.$100\times$Final Rating | ||||

Damodaran | $3$ | Rs.$1300$ | Rs.$150\times$Final Rating | ||||

Eman | $2$ | Rs.$1100$ | Rs.$200\times$Final Rating |

The following additional facts are known.

- Arun and Barun have got a rating of $5$ in exactly one of the parameters. Chandan has got a rating of $5$ in exactly two parameters.
- None of drivers has got the same rating in three parameters.

If all five drivers got bonus, what is the maximum possible value of the monthly payment (in rupees) that a driver gets?

- $1960$
- $1950$
- $1900$
- $2050$