Question

Deveshi has a total of 590 as currency notes in the denominations of
750,20 and 10. The ratio of the number of 50 notes and 20 notes is 3:5. If she has
a total of 25 notes, how many notes of each denomination she has?

Give me a proper answer!!!
​

Answer 1

Given:

Deveshi has a total of 590 as currency notes in the denominations of 750,20 and 10.

Ratio of the number of 50 notes and 20 notes is 3:5.

⠀

To find:

Notes of each denomination she has?

⠀

Solution:

★ Let the number of Rs.50 notes and Rs.20 notes be 3x and 5x, respectively.

But she has 25 notes in total.

Therefore,

the number of Rs.10 notes = $\tt{25 - (3x + 5x) = 25 - 8x}$

The amount she has

$\star{\boxed{\sf{\orange{from\: Rs.50\: notes: 3x × 50 = Rs.150x}}}}$

$\star{\boxed{\sf{\purple{from\: Rs.50\: notes: 5x × 20 = Rs.100x}}}}$

$\star{\boxed{\sf{\green{from\: Rs.10\: notes: (25 - 8x) × 10 = Rs.(250 - 80x)}}}}$

★ Hence the total money she has:-

$\large{\tt{\longmapsto{150x + 100x + (250 - 80x)}}}$

$\large{\tt{\longmapsto{Rs.(170x - 250)}}}$

But she has Rs.590.

Therefore,

$\large{\tt{\longmapsto{170x + 250 = 590}}}$

$\large{\tt{\longmapsto{170x = 590 - 250 = 340}}}$

$\large{\tt{\longmapsto{x =\dfrac{340}{170} = 2}}}$

The number of Rs.50 notes she has = $\large{\tt{3x}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\large{\tt{= 3 × 2 = 6}}$

The number of Rs.20 notes she has = $\large{\tt{5x}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\large{\tt{= 5 × 2 = 10}}$

The number of Rs.10 notes she has

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\large{\tt{= 25 - 8x}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\large{\tt{= 25 - (8 × 2)}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\large{\tt{= 25 - 16 = 9}}$

★ Hence, there are 9 notes of each denomination she has.

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