Question

A sum of Rs 500 is in the form of denimination of Rs 5 and Rs 10.if the total number of notes is 90. find the no of notes of each type. Write the statement also not write inly answer​

Answer 1

GIVEN :–

• A sum of Rs 500 is in the form of denimination of Rs 5 and Rs 10.

• Total number of notes = 90.

TO FIND :–

• No of notes of each type = ?

SOLUTION :–

• Let the number of notes of 5 rupees = x

• And the number of notes of 10 rupees = y

▪︎ According to first condition –

$\\ \implies { \bold{5x + 10y = 500}}$

$\\ \implies { \bold{5(x + 2y) = 500}}$

$\\ \implies { \bold{x + 2y= \cancel \dfrac{500}{5}}}$

$\\ \implies { \bold{x + 2y= 100}}$

$\\ \implies { \bold{x = 100 - 2y \: \: \: - - - eq.(1)}}$

▪︎ According to the second condition –

$\\ \implies { \bold{x + y = 90}}$

$\\ \implies { \bold{(100 - 2y) + y = 90 \: \: \: \: \: \: [ \: using \: \: eq.(1)]}}$

$\\ \implies { \bold{100 -y = 90 }}$

$\\ \implies { \bold{ y = 100 - 90}}$

$\\ \implies \large{ \boxed{ \bold{ y = 10}}}$

• Put the value of 'y' in eq.(1) –

$\\ \implies { \bold{x = 100 - 2(10)}}$

$\\ \implies { \bold{x = 100 - 20}}$

$\\ \implies \large{ \boxed{ \bold{x = 80}}}$

▪︎ Hence , Number of notes of five rupees is 80 and Number of notes of ten rupees is 10.

Answer 2

Given that :-

Total amount of money is rs 500 .

Money is in denomination of Rs 50 and Rs 10 notes .

Total number of notes is 90 .

To Find :-

Number of each type of note .

Solution :-

Let's assume that we have x number of 5 rupee notes and y number of 10 rupee notes .

According to the question total notes is 90 .

$\sf{ \implies x + y = 90 }$

$\sf{\implies x = 90 - y }$

And sum of money is 500 .

$\sf{\implies 5x + 10y = 500 }$

Putting the value of x here .

$\sf{\implies 5[90-y] + 10 y = 500 }$

$\sf{\implies 450 - 5y + 10y = 500 }$

$\sf{\implies 5y = 500 - 450 }$

$\sf{\implies y = \frac{50}{5 } \rightarrow 10}$

Number of 10 rupee notes is 10 .

$\sf{\implies x = 90 - 10 }$

$\sf{\implies x = 80\; notes }$

And number of 5 rupee notes is 80 .