Question

A boy has x coins of 50 paise each, 2x coins of 25 paise each, 4x coins of 10 paise each and 8x coins of 5 paise each. Find the number of 5 paise coins if the value of all the coins is Rs.9?
(a) 40
(b) 20
(c) 500
(d) 300

Answer 1

Hint: We start solving the problem by converting the total amount that boy has into paise by using the conversion Rs.1 = 100 paise. We then multiple the number of coins with their respective values and add them together. We then equate this obtained result of addition with the money that the boy possesses to get the value of x. We then use this value to find the total number of 5 paise coins present with the boy.

Complete step by step answer:
According to the problem, we are given that a boy has x coins of 50 paise each, 2x coins of 25 paise each, 4x coins of 10 paise each and 8x coins of 5 paise each. We need to find the 5 paise coins if the value of all the coins is Rs.9.
We know that Rs.1 = 100 paise. So, the boy has the total value of all the coins as $9\times 100=900$ paise.
Now, let us add the value of all the coins present with the boy.
So, we get $\left( x\times 50 \right)+\left( 2x\times 25 \right)+\left( 4x\times 10 \right)+\left( 8x\times 5 \right)=900$.
$\Rightarrow 50x+50x+40x+40x=900$.
$\Rightarrow 180x=900$.
$\Rightarrow x=\dfrac{900}{180}$.
$\Rightarrow x=5$.
Now, let us find the total number of 5 paise coins present with the boy. So, we get $8x=8\times 5=40$ coins each of 5 paise.

So, the correct answer is “Option a”.

Note: Whenever we get this type of problems, we first try to convert the given values into a common unit to avoid confusion and calculation mistakes. We should not stop solving the problem after finding the value of x, which is the most common mistake that many students make. We can also do this problem by converting paise to rupees which require good precision in calculation. Similarly, we can expect problems to find the percentage of the value of 5 paise coins that contribute to the total amount.