Question

Katha has coins in the denomination of ₹2, ₹5 and ₹ 10. The number of ₹2 coins is 3 times the number of ₹5 coins and total number of coins is 160. If the total amount of coins is ₹730, how many coins of each denomination does Katha have?

Please help!!

Answer 1

2Rs-90 5Rs-30 10Rs-40

Answer 2

GIVEN :-

• Katha have denominations of 2rs,5rs and 10rs.

• 2 coins is three times the number of 5

• total no of coins 160

• total amount of coins is rs 730

TO FIND :-

• no of coins of each denomination does Katha have

SOLUTION :-

let the number of 5rs coins be x

HENCE ,

$\rm{no \: of \: 2 \: rs \: coins \: =3x }$

$\rm{total \: no \: of \: coins \: =160 }$

so,

$\rm{no \: of \: 10 \: rs \: coins =160 - 3x - x }$

$\rm{no \: of \: 10 \: rs \: coins =160 - 4x }$

now according to question :-

$\implies \rm{5(x) + 2(3x) + 10(160 - 4x) = 730}$

$\implies \rm{5x + 6x+ 1600 - 40x = 730}$

$\implies \rm{11x + 1600 - 40x = 730}$

$\implies \rm{11x - 40x = 730 - 1600}$

$\implies \rm{- 29x = - 870}$

$\implies \rm{x = \dfrac{ - 870}{ - 29} }$

$\implies \rm{ \bf \: x = 30}$

now ,

$\implies \rm{no \:of \: 5 \: rs \: coins = x}$

$\implies \boxed{\rm{no \:of \: 5 \: rs \: coins = 30}}$

$\implies \rm{no \:of \: 2 \: rs \: coins = 3x}$

$\implies \boxed {\rm{no \:of \: 2 \: rs \: coins = 90}}$

$\implies \rm{no \:of \: 10 \: rs \: coins = 160 - 4x}$

$\implies \rm{no \:of \: 10 \: rs \: coins = 160 - 120}$

$\implies \boxed{ \rm{no \:of \: 10 \: rs \: coins = 40}}$