Question

A sum of rs.45 is made up of 100 coins of 50 paise and 25 paise denominations. What is the ratio of the number of 50 paise to those of 25 paise ?

Answer 1

$\bold{given : } \\ \\ there \: are \: total \: 100 \: coins \: \\ \\ some \: are \: of \: 25 \: paise \\ \\ some \: are \: of \: 50 \: paise \: \\ \\ \\ \\ \bold{let} \\ \\ no. \: of \: 50 \: paise \: coins : \\ \\ \: = > \bold{x }\: \\ \\ no. \: of \: 25 \: paise \: coins : \\ \\ = > \: \bold{y }\: \\ \\ \\ \\ \:\bold{ by \: given \: conditions : } \\ \\\bold {x \: + \: y = 100.......................1} \\ \\ \\ \\ 50x + 25y = 45 \: rs \: \\ \\ 50x + 25y = 4500 \: paise \: \\ \\ divide \: by \: 25 \: \\ \\\bold {2x + y = \: 180 .......................2}\\ \\ \\ \\ substract \: equation \: 1 \: from \: 2 : \\ \\ 2x + y = 180 \\ - \\ x + y = 100 \\ - - - - - - - \\ \\ \bold{x = 80} \\ \\ \\ \\ put \: x \: = \: 80 \: in \: equation \: 1 \\ \\ x + y = 100 \\ \\ 80 + y = 100 \\ \\ y = 100 - 80 \\ \\ \bold{y = 20} \\ \\ \\ \\ \bold{there \: are \: 80 \: coins \: of \: 50 \: paise} \: \\ \\ \: \bold{20 \: coins \: of \: 25 \: paise}$