case /data -based (4 Marks)

Question 14 Marks

In an archery game, the points scored on hitting a circular region on a board is shown in the figure below.

No point is given when an arrow missed the board. Sharmistha scored only 6 or 4 points in a game. The number of times she scored 6 is five more than the number of times she scored 4 . She scored 80 points in the game.
Q.1. Which of the following equation represents Sharmistha's score?
(a) $6 x+4 x=80$ $\qquad$ (b) $6 x+4(x+5)=80$
(c) $6(x-5)+4 x=80$ $\qquad$ (d) $6 x+4(x-5)=80$
Q.2. How many arrows did Sharmistha shoot?
(a) 10 $\qquad$ (b) 11 $\qquad$ (c) 15 $\qquad$ (d) 30
Q.3. Which of the following equations does $x=5$ not satisfy?
(a) $2 x-1=9$ $\qquad$ (b) $3 x+4=19$
(c) $3 x+1=13$ $\qquad$ (d) $4 x-3=17$

Answer

1. (D). 6 x+4(x-5)=80
Let the number of times she scored 6 be $x$.
According to the question, the number of times she scored 6 is five more than the number of times she scored 4 . And she scored 80 points total.
$
\therefore 6 x+4(x-5)=80
$
2. (A). From above equation,
$6 x+4(x-5)=80$
$\Rightarrow 6 x+4 x-20=80$
$\begin{array}{lrl}\Rightarrow
10 x
=100 \\ \therefore
x
=10\end{array}$
Thus, Sharmistha shoot the 10 arrows.
3. (C). For $x=5$,
(a) $2 x-1=9$
$\Rightarrow 2(5)-1=9$
$\begin{aligned} 10-1 & =9 \\ \text { LHS } & =\text { RHS }\end{aligned}$
$x=5$ satisfies the equation.
(b) $3 x+4=19 \Rightarrow 3(5)+4=19$
19=19
LHS =RHS
$x=5$ satisfies the equation.
(c) $3 x+1=13 \Rightarrow 3(5)+1=16$
$
16 \neq 13
$
LHS $\neq$ RHS, $x=5$ does not satisfies the equation.
(d) $4 x-3=17 \Rightarrow 4(5)-3=17$
17=17
LHS $=$ RHS, $x=5$ satisfles the equation.

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Question 24 Marks

Multiple gaming tournaments can be played online. In these games, players can compete with players from any part of the world.
In a tournament, 200 points are awarded for a win and 20 points are deducted for a loss.
Q.1. Chetan participated in the tournament.
He won two more matches than the number of matches he lost.
He scored 1120 points.
How many matches did he play?
(a) 6 $\qquad$ (b) 8 $\qquad$ (c) 10 $\qquad$ (d) 14
Q.2. Which of the following represents an equation in one variable?
(a) $5 p+3$ $\qquad$ (b) $4+2 a$ $\qquad$ (c) $5+7=12$ $\qquad$ (d) $5+4 x=9$
Q.3. Diksha played 16 matches in a tournament. The number of matches won was equal to the number of matches lost by her.
How many points did she score?
Q.4. Drishti and Raghav also participated in the tournament.
Drishti won 10 more matches than the number of matches she lost. Her score was 6140 points.
Raghav lost 15 more matches than the number of matches he won. His score was 6000 points.
Who played more matches? Justify your answer.

Answer

1. (C). 10
Let the number of matches lost be $x$.
Then, number of matches won $=x+2$
According to the question,
$
\begin{array}{l}
200(x+2)+(-20) x=1120 \\
180 x=1120-400=720 \\
\therefore \quad x=\frac{720}{180}=4
\end{array}
$
$\therefore$ Number of matches played $=x+x+2$
$
\begin{array}{l}
=2 x+2 \\
=2(4)+2=10
\end{array}
$
2. (D). $5+4 x=9$
3. Diksha played total 16 matches and the number of matches won is equal to the number of matches lost by her.
$

\begin{aligned}\text { Therefore, }
200(8)+8(-20) & =1600-160 \\
& =1440 \text { points }
\end{aligned}
$
Thus, Diksha scored 1440 points.
4. For Drishti,
Let the number of matches she lost $=x$
and the number of matches she won $=x+10$
According to the question,
$
\begin{aligned}
200(x+10)+x(-20) & =6140 \\
200 x+2000-20 x & =6140 \\
2000+180 x & =6140 \\
180 x & =6140-2000 \\
x & =\frac{4140}{180} \\
x & =23
\end{aligned}
$
$\therefore$ Diksha played the number of matches
$
\begin{array}{l}
=x+x+10=2 x+10 \\
=2(23)+10=46+10=56
\end{array}
$
For Raghav,
Let the number of matches he won $=y$
and the number of matches he lost $=y+15$
According to the question,
$
\begin{aligned}
200 y+(-20)(y+15) & =6000 \\
200 y-20 y-300 & =6000 \\
180 y & =6000+300 \\
180 y & =6300 \\
y & =\frac{6300}{180} \\
y & =35
\end{aligned}
$
$\therefore$ Raghav played the number of matches
$\begin{array}{l}=y+y+15=2 y+15 \\ =2(35)+15 \\ =70+15=85\end{array}$
Therefore, Raghav played 85 matches which is more

than the 56 matches played by Diksha.

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MATHS case /data -based (4 Marks)

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