Question

Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50. The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5. If she has a total of 30 notes, how many notes of each denomination she has.​

Answer 1

Given that,

Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50.

The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5.

She has a total of 30 notes with her.

Let assume that

Number of Rs 10 notes be 2x

Number of Rs 20 notes be 5x

Number of Rs 50 notes be 30 - (2x + 5x) = 30 - 7x

So,

`\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad\sf \:Denomination \: of \: Rs \: 10=2x\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=5x\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=30 - 7x\end{aligned}} \qquad \\ \\ \end{gathered}`

Now,

Amount in form of Rs 10 = 10 × 2x = Rs 20x

Amount in form of Rs 20 = 20 × 5x = Rs 100x

Amounts in form of Rs 50 = 50 × (30 - 7x) = Rs 1500 - 350x

Now, According to statement

`\begin{gathered}\sf \: 20x + 100x + 1500 - 350x = 1040 \\ \\ \end{gathered}`

`\begin{gathered}\sf \: 120x + 1500 - 350x = 1040 \\ \\ \end{gathered}`

`\begin{gathered}\sf \: 1500 - 230x = 1040 \\ \\ \end{gathered}`

`\begin{gathered}\sf \:- 230x = - 460 \\ \\ \end{gathered}`

`\sf \: \implies x = 2`

Hence,

`\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:Denomination \: of \: Rs \: 10=4\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=10\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=16\end{aligned}} \qquad \\ \\ \end{gathered}`

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