Question

Express the given ratios in their simpler form:
175 paisa: 5 rupees 25 paise.

Answer 1

Hint: In this question, we need to simplify the given ratio of money in paisa and rupees. For this, we will first convert both the given numbers into the same form i.e. paisa. Then we will write them in division form and simplify the division. Then we will write ratio which will be the ratio in simplest form. We will use that 1 rupee = 100 paise.

Complete step-by-step solution
Here, we are given numbers as 175 paise and 5 rupees 25 paise. Since we need to find their ratio in the simplest form, so they should be in the same units.
Let us convert both units into paisa only.
Now we know that 1 rupee is equal to 100 paise, so 5 rupees will become equal to $5\times 100=500$ paisa. Now we are given a number as 5 rupees 25 paise. Hence, 5 rupees 25 paise becomes equal to $500+25=525$ paisa. So, now we need to find the simplest ratio between 175 paise: 525 paise. i.e. we need to find the simplest ratio between 175:525. As we know that, any ratio can be written in division form, so we can write 175:525 as $\dfrac{175}{525}$.
Now let us simplify it.
Dividing the numerator and denominator by 5 we get $\dfrac{175\div 5}{525\div 5}=\dfrac{35}{105}$.
Again, dividing the numerator and denominator by 5, we get $\dfrac{35\div 5}{105\div 5}=\dfrac{7}{21}$.
Now, dividing the numerator and denominator by 7, we get $\dfrac{7\div 7}{21\div 7}=\dfrac{1}{3}$.
Therefore, the reduced form of $\dfrac{175}{525}$ is $\dfrac{1}{3}$.
Hence, our required ratio becomes 1:3.

Note: Students should always make the units of given numbers the same to calculate the simplified ratio. To check the divisibility, they can use divisibility rules also. According to divisibility rule 5, the digit at one place should be 0 or 5. The divisibility rule of 3 states that the sum of the digits of a number is itself divisible by 3.