Direction : The table given below shows the data about track record of car…
2021
Direction : The table given below shows the data about track record of car racing game, where 4 cars P, Q, R and S are competing to reach finishing line which is at a distance of 3000 m from their initial starting point.
1. Drift refers to oversteering intentionally done by the driver.
2. While calculating average speed, do not consider time taken in drift/crash.
3. Points = 50 × drifts – 20 × crashed
In order to gain 10 more points than car S, how many total drifts should car P have made, if car P’s time and number of crashes remain same.
- A.
5
- B.
3
- C.
10
- D.
8
- E.
7
Attempted by 1 students.
Show answer & explanation
Correct answer: E
Concept
A linear scoring rule gives each competitor a score from two weighted counts. Here Points = 50 × (drifts) − 20 × (crashes). To hit a TARGET score when one of the two counts is fixed, isolate the free count: write the points equation, substitute the known fixed count, set the expression equal to the target, and solve the resulting linear equation for the unknown count.
Application to this item
Read Car S from the table: drifts = 8, crashes = 6. Its points = 50 × 8 − 20 × 6 = 400 − 120 = 280.
Car P must score 10 more than Car S, so Car P's target = 280 + 10 = 290.
Car P's crashes stay fixed at 3. Let D be Car P's required drifts. Apply the rule: 50 × D − 20 × 3 = 290, i.e. 50D − 60 = 290.
Solve the linear equation: 50D = 290 + 60 = 350, so D = 350 ÷ 50 = 7.
Cross-check
With D = 7 and the unchanged 3 crashes, Car P's points = 50 × 7 − 20 × 3 = 350 − 60 = 290, which is exactly 280 + 10 = Car S's points + 10. So Car P needs 7 total drifts.