Question

60 passengers are travelling in a bus.Some passengers are carrying rupees 5 tickets and remaining are carrying rupees 10 tickets.the total fare received by the conductor is rupees 405.find the number of passengers carrying rupees 5 ticket & rupees 10 tickets

Answer 1

$\sf\large\underline{Let:-}$

$\tt{\implies Number\:P\:Rs5=x}$

$\tt{\implies Number\:P\:Rs10=60-x}$

$\sf\large\underline{Given:-}$

$\tt{\implies Total\:amount=405}$

• According to question:-

$\tt{\implies 5*x+(60-x)*10=405}$

$\tt{\implies 5x+600-10x=405}$

$\tt{\implies -5x+600=405}$

$\tt{\implies 5x=600-405}$

$\tt{\implies 5x=195}$

$\tt{\implies x=39}$

• Therefore,

$\tt{\implies Number\:P\:Rs5=x=39}$

$\tt{\implies Number\:P\:Rs10=60-x=60-39=21}$

Answer 2

$\sf\large\underline\blue{Let:-}$

$\tt{\implies The\: Number\: passengers\:_{(Rs.5)}=x}$

$\tt{\implies The\: Number\: passengers\:_{(Rs.10)}=y}$

$\sf\large\underline\blue{Given:-}$

$\tt{\implies Amount\: received\:_{(by\:conductor)}=R.s405}$

$\sf\large\underline\blue{To\: Find:-}$

$\tt{\implies The\: Number\: passengers\:_{(Rs.5)}=?}$

$\tt{\implies The\: Number\: passengers\:_{(Rs.10)}=?}$

$\sf\large\underline\blue{Solution:-}$

To calculate the number of of passengers who is traveling in a bus. At first we have to set up equation as per the given clue in the question. As you can see in the given question that Some passengers are carrying rupees 5 tickets and remaining are carrying rupees 10 tickets.the total fare received by the conductor is rupees 405.

$\tt{\implies Passenger\:_{(Rs.5)}+Passenger\:_{(Rs.10)}=Passenger\:_{(total)}}$

$\tt\green{\implies x+y=60-----(i)}$

$\tt{\implies Cost\:_{(passenger\:Rs.5)}+Cost\:_{(passenger\:Rs.10)}=Total\:_{(amount)}}$

$\tt\green{\implies 5x+10y=405----(ii)}$

• In eq (i) multiplying by 5 then subtracted eq (ii):-

$\tt{\implies 5x+10y=405}$

$\tt{\implies 5x+5y=300}$

• By calculating we get here:-

$\tt{\implies 5y=105}$

$\tt{\implies y=21}$

• Putting the value of y=21 in eq (i) :-

$\tt{\implies x+y=60}$

$\tt{\implies x+21=60}$

$\tt{\implies x=60-21}$

$\tt{\implies x=39}$

$\sf\large{Hence,}$

$\tt{\implies The\: Number\: passengers\:_{(Rs.5)}=39}$

$\tt{\implies The\: Number\: passengers\:_{(Rs.10)}=21}$