Question

A certain number of one rupee, fifty paise and twenty five paisa coins are in the ratio of 2.5:3:4, add up to rs.210.how many 50 paisa coins were there?

Answer 1

Let x be the normalizing factor for the ratio
So,
number of 1 rupee coins= 2.5x
number of  50 paise coins=3x
number of  25 paise coins=4x
Now,
50 paise is 1/2  of one rupee
25 paise is 1/4 of one rupee


The sum of these currencies add upto 210 so,
2.5x+ (3x)/2 + (4x)/4 = 210
2.5x + (3x)/2 + x= 120
x=(210)/(2.5+ 3/2 +1)
x=42
So,
number of 50 paise coins= 3x
                                         =3*42
                                         =126
SO,
There are 126  fifty paise coins

Answer 2

Let the common ratio be x.

Then, the total number of 1-rupee coins = 2.5x

Then, the total number of 50-paise coins = 3x

Then, the total number of 25-paise coins = 4x


Now,

Given that total number of coins add up to 210.

= > 2.5x + 0.5 * 3x + 0.25 * 4x = 210

= > 2.5x + 1.5x + 1x = 210

= > 5x = 210

= > x = 42.

Number of 50-paise would be = 3(42)

                                                   = 126.



Therefore the total number of 50 paisa coins = 126.



Hope this helps!