Question

A sum of Rs. 500 is in the form of denomination of Rs.5and Rs. 10. If notes of notes is 90.Find the number of each type. ​

Answer 1

$\bf{\underline{\underline \green{Solution:-}}}$

$\mathsf {Let \:the \:number \:of\: 5 \:Rupee\: note\: = \:x}$

$\mathsf {Then \:the\: number \:of \:10 \:Rupee \:note \:= \:90\: - \:x}$

$\mathsf {Total \:money\: =\:Rs. 500}$

$\underline\mathtt \orange{As \:per \:the \:given\: condition,}$

$\longrightarrow \sf \red {5x + 10(90 - x) = 500}$

$\longrightarrow \sf \pink {5x + 900 - 10x = 500}$

$\longrightarrow \sf \green {-5x = -400}$

$\longrightarrow \sf \blue { x = 80}$

$\underline\mathtt \orange{Hence:}$

• $\small\red{\underline {\boxed{\sf\green{ Number \:of\: 5 \:Rupee\: note \:= \: 80} }}}$

$\underline\mathtt \orange{And,}$

• $\small\red{\underline {\boxed{\sf\green{Number \:of\: 10 \:Rupee \:note = (90 - 80) = 10} }}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Answer 2

Given

A sum of Rs. 500 is in the form of denomination of Rs.5and Rs. 10. If notes of notes is 90.

To find

• The number of each type of notes

Solution

★ Let the Rs.5 note be x and Rs.10 be y

*According to the given condition*

✡Total amount of Rs.5 and Rs.10 notes = 500

• 5x + 10y = 500 -----(i)

✡Number of Rs.5 and Rs.10 notes = 90

• x + y = 90 ------(ii)

Multiply (i) by 1 and (ii) by 10

• 5x + 10y = 500
• 10x + 10y = 900

Subtract both the equations

➡ (5x + 10y) - (10x +10y) = 500 - 900

➡ 5x + 10y - 10x -10y = - 400

➡ -5x = -400

➡ x = 400/5 = 80

Putting the value of x in eqⁿ (ii)

➡ x + y = 90

➡ 80 + y = 90

➡ y = 90 - 80 = 10

Therefore,

$\large{\boxed{\bf{\blue{Number\:of\:Rs.5 \:note = 80}}}}$

$\large{\boxed{\bf{\blue{Number\:of\:Rs.10\:note = 10}}}}$