The table below gives some information about the points scored by Arjun in AHC (All Hastin Championship), in each of five different mind games-Dice, Dance, Dupe, Digit and Dynasty.

Game

Total Problems

Problems Attempted

Successful Attempts

Failures

Net Score

Dice

35

29

Dance

30

Dupe

35

17

Digit

40

11

Dynasty

45

30

It is also known that,

for every successful attempt Anon gets one point and for every unattempted problem he loses 1/6^{th} of a point and for every failure he loses 1/3rd of a point.

Arjun scored a total of 67 points end attempted 125 problems

the number of failures of Arjun in Digit is 1/6th of his total number of failures and twice his number of failures in Dance.

Adonis net score in Dance is double that in Dupe.

Q1. What is the total number of failures of Arjun in the competition?

Q2. The maximum number of failures of Anun in any game was

Q3. What is the number of problems attempted by Arjun in Dance?

Q4. What is the net score of Arjun in Dynasty?

Q1. Ans: (36)

Q2. Ans: (12)

Q3. Ans: (18)

Q4. Ans: (26)

Given,

Arjun attempted 125 problems and got 67 points i.e., he already lost $60 \times 1 / 6 = 10$ points for unattempted problems and for every failure he loses another 4/3 (1 mark of the question and 1/3 rd negative marks) points of this 115 points.

$125 - 10 - \frac { 4 } { 3 } ( F ) = 67$

$F = 36$

Total successful attempts $= 125 - 36 = 89$

In Dupe, number of successful attempts $= 17 - 6 = 11$

Now, sum of number of unattempted problems and successful attempts in Digit is 34 and as the total score in Digit is a integer. the number of unattempted problems must be a multiple of 6.

By trail and error,

Number of unattempted problems = 18

Number of attempted problems = 22

Number of successful attempts = 16

Net score = 11

Number of failures in Dance = 3

Net score = 12

By trail and error,

Number of unattempted problems. which must be a multiple of 6= 12