Question

A bag contains a total of 105 coins of rs 1.50 paise and 25 paise denomination.
Find the total number of coins of rs 1 if there are total of 50.50 rupees in the bag and it is known that the number of 25 paise coin is 133.33% more than the number of rs 1 coin

Answer 1

Solution :-

Let the 1 rupee coin be 'x', 50 paise coin be 'y' and 25 paise coin be 'z'

Total number of coins = 105

So, x + y + z = 105 ............................(1)

Value of these coins = x/1 + y/2 + z/4 = 50.5

⇒ Taking L.C.M. of denominators and solving it, we get.
4x + 2y + z = 202 ...............................(2)

Now, subtracting (1) from (2) and eliminating z, we get.

  4x + 2y + z = 202
   x  +  y  + z = 105
-      -       -      -
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  3x + y         = 97 ..................(3)
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Now, as given in the question that number of 25 paise coins is 133.33 % more that of number of 1 rupee coin.

Therefore,

z = x/1 + 4x/3
Taking L.C.M. of denominators ans solving it, we get 
z = 7x/3
Putting the value of z = 7x/3 in equation (1), we get

x/1 + y/1 + 4x/3 = 105/1

Taking L.C.M. of denominators and solving it, we get.

3x + 3y + 7x = 315
10x + 3y = 315 .....................(4)

Now, multiplying (3), we get.
(3x + y = 97)*3 = 9x + 3y = 291 ..............(5)
subtracting (5) from (4), we get.

  10x + 3y = 315
    9x + 3y = 291   
  -      -         -
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    x         =    24
________________

So, number of 1 rupee coin is 24.

Putting x = 24 in equation (3)
3x + y = 97
3*24 + y = 97
72 + y = 97
y = 97 - 72
y = 25

Number of 1 rupee coin is 24. number of 50 paise coin is 25, then remaining are 25 paise coins.
25 paise coins are = 105 - (24 + 25)
= 56
Number of 25 paise coin is 56.