Question

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Meena went to a bank to withdraw Rs.2000. She asked the cashier to give Rs. 50 and Rs. 100 notes only . Meena got 25 notes in all . Find how many notes of Rs.50 and Rs.100 she received

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Answer 1

$\huge\underbrace\mathfrak\color{lime}{ †\: Question:–}$

Meena went to a bank to withdraw Rs.2000. She asked the cashier to give Rs. 50 and Rs. 100 notes only . Meena got 25 notes in all . Find how many notes of Rs.50 and Rs.100 she received

$\huge\underbrace\mathfrak\color{lime}{ †\: Answer:–}$

Let 'x' be the $ 50 notes

Let 'y' be the $ 100 notes

so ; x + y

Given that

Meena got 25 notes in all

x + y = 25

According to the problem ;

$~~~~~~~~~~~~~\longrightarrow$$\bold{x + y = 25}$ ----------(1)

$~~~~~~~~~~~~~\longrightarrow$$\bold{50x + 100y = 2000}$

$~~~~~~~~~~~~~\longrightarrow$$\bold{50 (x + 2y) = 2000}$

$~~~~~~~~~~~~~\longrightarrow$$\bold{x + 2y =\frac{2000}{50}}$

$~~~~~~~~~~~~~\longrightarrow$$\bold{x + 2y = 40}$ -----------(2)

Solving eq(1) and (2)

$~~~~~~~~~~~~~~~~x + y = 25$

$~~~~~~~~~~~~~~~~x + 2y = 40$

$~~~~~~~~~~~~~~(-)~(-)~~~(-)$

$~~~~~~~~~~~~~~~~-----------$

$~~~~~~~~~~~~~~~~~~- y = -15$

$~~~~~~~~~~~~~~~~-----------$

$~~~~~~~~~~~~~~~~~~\cancel{-} y = \cancel{-}15$

$~~~~~~~~~~~~~~~~~~y = 15$

$~~~~~~~~~~~~~~~~Substitute \:y = 15 \:in \:eq(1)$

$~~~~~~~~~~~~~\longrightarrow$$\bold{x + 15 = 25}$

$~~~~~~~~~~~~~\longrightarrow$$\bold{x = 25 - 15}$

$~~~~~~~~~~~~~\longrightarrow$$\bold{x = 10}$

The number of $ 50 notes is = 10

The number of $ 100 notes is = 15

Answer 2

Question :

Meena went to a bank to withdraw Rs 2000. She asked the cashier to give Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.

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Answer :

Rs 50 notes = 10 and Rs 100 notes = 15

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Solution :

Let total Rs 50 notes = x

and total Rs 100 notes = y

∴ Total notes = x+y

But we are given total notes = 25

$\sf \implies x+y = 25 \: \: - ①$

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Now, Meena has total money =50x + 100y

But we are given total money =Rs 2000

$\sf \implies 50x+100y=2000$

$\sf \implies 50(x+2y)=2000$

$\sf \implies x+2y = \dfrac{2000}{50}$

$\sf \implies x+2y = \dfrac{\cancel{2000}^{40}}{\cancel{50}}$

$\sf \implies x+2y = 40 \: \: - ②$

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On substraction of ① and ②,

(x+y) - (x+2y) = 25 - 40

x + y - x - 2y = - 15

- y= - 15

$\boxed{\sf y = 15}$

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Now, by putting y in ①,

x+y=25

x + 15 = 25

x = 25 - 15

$\boxed{\sf x=10}$

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∴ Rs 50 notes, x = 10

and Rs 100 notes, y = 15