Question

Every time a man hits the target he gets one rupee and every time he misses the target he has to pay the rupee. He is allowed to try 100 times and gets an amount of Rs. 30. How many times did he hit the target? ( A ) 70 ( B ) 60 ( C ) 75 ( D ) 65

Answer 1

Answer :-

Option d) 65

____________________

Let the -

• a number of targets he hit are x.

Given that a total number of targets are 100.

→ Hit targets = x

→ Missed target = 100 - x

Now,

He got Rs. 1 when he hit the target. But at the same time he losses Rs. 1 too, whenever he miss the target.

$\sf{For\:Rs.\:1}$

→ Hit target = 1(x)

= Rs. x

→ Missed target = 1(100 - x)

= 100 - x

Now, we have -

• Rupees gain by man = Rs. x

• Rupees loss by man = Rs. (100 - x)

• The total amount of rupees (money) he got = Rs. 30

Rupees gain by man - Rupees loss by man = Received rupees

According to question,

$\implies$ x - (100 - x) = 30

$\implies$ x - 100 + x = 30

$\implies$ 2x = 30 + 100

$\implies$ 2x = 130

$\implies$ x = 65

•°• He hit the target 65 times.

Answer 2

$\large\underline\mathfrak{Answer-}$

Option (D) 65

___________________

$\large\underline\mathfrak{Explanation-}$

Let us suppose the number of targets hit by him be n.

Also, the total number of targets = 100 ( Given )

So, missed targets = 100 - n

Now, as mentioned in the question, man got 1 rupee when he hit the target and loss 1 rupee when he miss the target.

$\implies$ Hit target = 1 × n => n

$\implies$ missed target = 1( 100 - n ) => 100 - n

$\Therefore$ Man gained rupees n and loss (100-n) rupees.

Total rupees = 30 Rs ( Given )

Recieved rupees = Gained rupees - loss rupees

A.T.Q,

$\implies$ n - (100 - n) = 30

$\implies$ n - 100 + n = 30

$\implies$ n + n = 30 + 100

$\implies$ 2n = 130

$\implies$ n = $\dfrac{130}{2}$

$\huge\boxed{n\:=\:65}$

Hence, Man hit the target 65 times.

Option ( D ) is correct.