Question

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

Answer 1

Solution :

Let no. of 50 rupee note be 3x and no. of 20 rupee note be 5x

According to Question :

No. of 50 rupee note + No. of 20 rupee note + No. of 10 rupee note = 25 notes

$\hookrightarrow \sf \: 3x + 5x + 10 \: rupee \: note = 25$

$\hookrightarrow \sf \: 8x + 10 \: rupee \: note = 25$

$\hookrightarrow \sf 10 \: rupee \: note = 25 - 8x$

50 rupee notes =

$\sf \: 3x \times 50 = 150x$

20 rupee notes =

$\sf \: 5x \times 20 = 120x$

10 rupee notes =

$\sf (\: 25 - 8x) \times 10 = 250 - 80x$

Given,

$\star \sf \: Total \: number = 25$

$\star \sf \: Total \:amount = 590$

Equation formed :

$\hookrightarrow \: \sf \: 150x + 100x + (250 - 80x) = 590$

$\hookrightarrow \sf \: 150x + 100x - 80x + 250 = 590$

$\hookrightarrow \sf \: 250x - 80x = 590 - 250$

$\hookrightarrow \sf \: 170x = 340$

$\hookrightarrow \sf \: x = \cancel\dfrac{340}{170}$

$\large \boxed{ \sf x = \: 2}$

Thus,

$\sf \: No. \: of \: 50 \: rupee \: note = \\ \sf 3x = 3 \times 2 = \boxed{ \sf \: 6}$

$\sf \: No. \: of \: 20 \: rupee \: note = \\ \sf 5x = 5 \times 2 = \boxed{ \sf \: 10}$

$\sf \: No. \: of \: 10 \: rupee \: note = \\ \sf 25 - 8x = 25 - 16 = \boxed{ \sf \: 9}$

Answer 2

Given :--

• Total currency = Rs.590
• Total Notes = 25
• Ratio of Rs.50 notes : Rs.20 notes = 3:5

To Find :---

• how many notes of each denomination she has ?

Solution :---

Let , She has Rs. 50 notes be 3x and Rs.20 notes be 5x .

So, Remaining Notes were of Rs.10.

→ Total notes given = 25

→ So, notes of Rs.10 = 25 - (3x + 5x) = (25 - 8x)

Now, Total money is given Rs. 590 ,

Hence,

→ 10(25-8x) + 20*5x + 50*3x = 590

→ 250 - 80x + 100x + 150x = 590

→ 170x = 590-250 = 340

→ x = 340/170 = 2 .

Hence,

→ Rs.50 notes = 3x = 3*2 = 6 notes .

→ Rs.20 notes = 5x = 5*2 = 10 notes .

→ Rs. 10 notes = (25-8x) = 25-8*2 = 9 notes ..

Verification :---

→ Rs.50 notes are 6 + Rs.20 notes are 10 + Rs.10 notes are 9

→ 50*6 + 20*10 + 10*9

→ 300 + 200 + 90

→ Rs.590 verified .

Hence, Deveshi has 6 notes of Rs.50, 10 notes of Rs.20 and 9 notes of Rs.10...

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