Question

A sum of rupees 2700 is two given in the form of 63 prizes if the prices of rupees hundred for rupees 25 find the number of prices of each type

Answer 1

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

• Total prizes = 63
• cost of all prizes = 2700

$\large\bf\underline \blue{To \: find:-}$

• Number of 100 rupees prizes and Number of 25 rupees prizes.

$\huge\bf\underline \red{Solution:-}$

Let the number of100 rupees prizes be x.

Let the number of 25 rupees prizes be y.

★ Total cost of prizes = Rs 2700

$: \implies \rm \:100x + 25y = 2700 \\ \\ \rm \: divide \: both \: side \: by \: 25 \: we \: get \\ \\: \implies \rm \:4x + y = 108........(i) \\ \\ \rm \: And \: Number \: of \: prizes \: of \: 100 \: and \: 25 \: rupees : \\ \\ : \implies \rm \:x + y = 63..............(ii)$

From eq. (ii),

$: \implies \rm \:y = 63 -x \: ...........(iii) \\ \\ \rm \:Substituting \: value \: of \: y\: in \: eq. \: (i) \\ \\ : \implies \rm \:4x+ 63 - x = 108 \\ \\ : \implies \rm \:3x = 108 - 63 \\ \\ : \implies \rm \:3x = 45 \\ \\ : \implies \rm \:x = \cancel\frac{45}{3} \\ \\ : \implies \bf \green{ x= 15} \\ \\ \rm \:putting \: value \: of \: x \: in \: eq. \: \: (iii) \\ \\ : \implies \rm \:y = 63 - x \\ \\ : \implies \rm \:y = 63 - 15 \\ \\ : \implies \bf \pink{y = 48}$

So,

The number of 100 rupees prizes = 15

The number of 25 rupees prizes = 48

Answer 2

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

• $\rm{The\: Number\:of\: price\:Rs.100=x}$
• $\rm{The\: Number\:of\: price\:Rs.25=63-x}$

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

• $\rm{The\: Number\:of\: price\:each\: types=?}$

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

• Given here,A sum of rupees 2700 is two given in the form of 63 prizes if the prices of rupees hundred for rupees 25]

$\bf\large\underline{A.T.Q:}$

$\rm{\implies 100(x)+25(63-x)=2700}$

$\rm{\implies 100x+1575-25x=2700}$

$\rm{\implies 100x-25x=2700-1575}$

$\rm{\implies 75x=1125}$

$\rm{\implies x=15}$

$\sf\large{Hence,}$

$\rm{\implies The\: Number\:of\: price\:Rs.100=x}$

$\rm{\implies The\: Number\:of\: price\:Rs.100=15}$

$\rm{\implies The\: Number\:of\: price\:Rs.25=63-x}$

$\rm{\implies The\: Number\:of\: price\:Rs.25=63-15}$

$\rm{\implies The\: Number\:of\: price\:Rs.25=48}$