Question

In a shooting competition, a marksman receives \[50paise\] if he hits the mark and pays \[20paise\] if he misses it. He tried \[60\]shots and was paid \[Rs1.30\]. How many times did he hit the mark?
A. \[19\]
B. \[22\]
C. \[18\]
D. \[21\]

Answer 1

Hint:Convert the money from paisa into rupees and then assume number of wins as a variable, using the information form an equation giving number of wins multiplied by money per win and subtract number of loss multiplied by money lost per loss and equate to the total amount he earned.

Complete step-by-step answer:
Since, we know \[1Rs = 100paise\]
Therefore, using unitary method we can find the value of multiple units if we are given value of a single unit
\[1paisa = Rs\dfrac{1}{{100}}\]
Therefore, multiplying \[50paise\] on both sides,
\[50paise = Rs\dfrac{1}{{100}} \times 50 = Rs0.5\]
Similarly, \[20paise = Rs\dfrac{1}{{100}} \times 20 = Rs0.2\]
Total number of shots taken by the marksman is \[60\]
Now, let us assume number of times marksman hits the mark as \[x\]
Then the number of times marksman missed the shot will be the number of hits subtracted from total number of shots.
Therefore, number of times marksman missed the shot is \[60 - x\]
We know from the question, total money earned by the marksman is \[Rs1.30\]
Money earned is sum of number of hits multiplied by money from one hit minus number of missed shots multiplied by money lost by one miss
Therefore, we can write the equation as
\[(x) \times (0.5) - (60 - x) \times (0.2) = 1.30\]
\[
  0.5x - 60(0.2) + 0.2x = 1.30 \\
  0.5x + 0.2x - 12 = 1.30 \\
  0.7x - 12 = 1.30 \\
 \]
Take all the constant values to RHS of the equation
\[
  0.7x = 1.30 + 12 \\
  0.7x = 13.30 \\
 \]
Divide both sides by \[0.7\]
\[
  \dfrac{{0.7x}}{{0.7}} = \dfrac{{13.30}}{{0.7}} \\
  x = \dfrac{{13.30}}{{0.7}} \\
 \]
Write the decimal numbers in the form of fractions by removing the decimal and dividing by number of zeros after the decimal.
\[
  x = \dfrac{{1330}}{{100}} \times \dfrac{{10}}{7} \\
  x = \dfrac{{133}}{7} \\
 \]
We can factorize \[133 = 19 \times 7\]
\[
  x = \dfrac{{19 \times 7}}{7} \\
  x = 19 \\
 \] { by cancelling out same terms from denominator and numerator}
Therefore, option A is correct.

Note: Students are likely to make the mistake of not converting the amount in one form which gives a wrong answer. Students are advised to convert the money from rupees to paisa or paise to rupees but all should be in one unit.