Question

A bag contains one-rupee, two-rupee, and five-rupee coins in the ratio 5 : 7 : 12 amounting to Rs. 395. Find the number of coins of each type.

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf \small A \: bag \: contains \: one \: rupee, two \: rupee, and \: five \: rupee \: coins \: in \: the \: ratio \: 5 : 7 : 12$

$\sf \implies Total \: value \: of \: all \: coins = Rs. \: 395$

$\bf \underline{\underline{\maltese\: To \: find }}$

$\sf \implies Number \: of \: coins \: of \: each \: type = \: ?$

$\bf \underline{\underline{\maltese\: Solution }}$

$\sf Let \: us \: assume \: that,$

$\sf \implies Number \: of \: one \: rupee \: coins = 5x$

$\sf \implies Number \: of \: two \: rupee \: coins = 7x$

$\sf \implies Number \: of \: three \: rupee \: coins = 12x$

$\bf \underline{Now},$

$\sf \implies Amount \: of \: one \: rupee \: coins = 5x \times 1 = 5x$

$\sf \implies Amount \: of \: two \: rupee \: coins = 7x \times 2 = 14x$

$\sf \implies Amount \: of \: three \: rupee \: coins =12x \times 5 = 60x$

$\bf \underline{ Therefore},$

$\sf \implies 5x + 14x + 60x = 395$

$\sf \implies 79x = 395$

$\sf \implies x = \cancel \dfrac{395}{79}$

$\sf \implies x = 5$

$\bf \underline{ Hence},$

$\sf \implies Number \: of \: one \: rupee \: coins = \bf5x = 5 \times 5 = 25$

$\sf \implies Number \: of \: two \: rupee \: coins = \bf 7x = 7 \times 5 = 35$

$\sf \implies Number \: of \: three \: rupee \: coins= \bf12x = 12 \times 5 = 60$