Question

A sum of ₹500 is in the form of denominations of ₹5 and ₹10 .If the total number of notes is 90,find the number of notes of each type.

Answer 1

Answer:

The number of ₹ 5 notes is 80 and that of ₹ 10 notes is 10.

Step-by-step-explanation:

Let the number of ₹ 5 notes be x.

And the number of ₹ 10 notes be y.

Now,

Total money of ₹ 5 notes = 5x

Total money of ₹ 10 notes = 10y

From the first condition,

Total amount of money of ₹ 5 and ₹ 10 notes is 500.

∴ 5x + 10y = 500

⇒ x + 2y = 100 - - - [ Dividing by 5 ]

⇒ x = 100 - 2y

⇒ x = - 2y + 100 - - - ( 1 )

From the second condition,

There are total 90 notes of ₹ 5 and ₹ 10.

∴ x + y = 90

⇒ ( - 2y + 100 ) + y = 90 - - - [ From ( 1 ) ]

⇒ - 2y + 100 + y = 90

⇒ - 2y + y = 90 - 100

⇒ - y = - 10

⇒ y = 10

∴ No. of ₹ 10 notes = 10

By substituting y = 10 in equation ( 1 ), we get,

x = - 2y + 100 - - - ( 1 )

⇒ x = - 2 * 10 + 100

⇒ x = - 20 + 100

⇒ x = 80

∴ No. of ₹ 5 notes = 80

∴ The number of ₹ 5 notes is 80 and that of ₹ 10 notes is 10.

Answer 2

$\underline{ \pink{ \rm GIVEN \: \: DATA\: \: : }}$

Sum of Denominations of ₹5 and ₹10 is ₹500

Sum of ₹5 and ₹10 , Total number of notes is 90 notes

$\underline{ \purple{ \rm TO \: \: FIND \: \: : }}$

Number of notes of Each Type .

$\underline{ \red{ \rm SOLUTION \: \: : }}$

Let number of notes of ₹5 be a

number of notes of ₹10 be b

so, Eqⁿs are :

$\rm 5a + 10b = 500$

$\rm a + 2b = 100$

$\rm \orange{\boxed{ \blue{ \rm a = 100 - 2b}}} \to \: eqn(1)$

and, second condition,

$\rm a + b = 90$

$\rm (100 - 2b) + b = 90 \: \: \: \: [from \: \: eqn(1) ]$

$\rm - b = - 10$

$\boxed{ \color{springgreen} \rm b = 10}$

then, Finding a

$\rm a = 100 - 2(10)$

$\rm a = 80$

$\underline{{ \color{red} \rm FINAL \: \: \: ANSWER \: }}:$

Number of ₹5 notes is 80 notes

Number of ₹10 notes is 10 notes