Question

in a cinema hall 300 tickets was sold for a total of rupees 32000 if the tickets were of two denominations of rupees 80 and 120 how many of each person​

Answer 1

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

• $\rm{Number\:of\: tickets=300}$
• $\rm{Total\:collection\:amount=Rs.32000}$

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

$\rm{\implies Let,\:The\: N\:of\:person\:who\: bought\:Rs.80\: tickets=x}$

$\rm{\implies The\: N\:of\: person\:who\: bought\:Rs.120\: tickets=y}$

$\sf\underline{Given\:in\:1st\:case:}$

$\rm{\implies sum\:of\:2\: tickets=Total\:tickets}$

$\rm{\implies x+y=300-------(ii)}$

$\sf\underline{Given\:in\:2nd\:case:}$

$\rm{\implies Sum\:of\:2\: denomination=32000}$

$\rm{\implies 80x+120y=32000-----(i)}$

• Now, solving equation i and ii here]

$\rm{\implies x+y=300}$

$\rm{\implies 80x+120y=32000}$

• in eq ii multiplying by 80 ]

$\rm{\implies 80x+120y=32000}$

$\rm{\implies 80x+80y=24000}$

• By solving we get here]

$\rm{\implies 40y=8000}$

$\rm{\implies y=200}$

• Putting the value of y=200 in eq ii]

$\rm{\implies x+y=300}$

$\rm{\implies x+200=300}$

$\rm{\implies x=300-200}$

$\rm{\implies x=100}$

$\sf\large{Hence,}$

$\rm{\implies The\: N\:of\:person\:who\: bought\:Rs.80\: tickets=100}$

$\rm{\implies The\: N\:of\: person\:who\: bought\:Rs.120\: tickets=200}$

Answer 2

Question:-

in a cinema hall 300 tickets was sold for a total of rupees 32000 if the tickets were of two denominations of rupees 80 and 120 how many of each person

by solving equation we get ,

The number of people who bought Rs.80 tickets=100

The number of people who bought Rs.120 tickets=200

Verification:-

=>80×100+120×200=32000

=>8000+24000=32000

=>32000=32000

Hence,proved