Question

Q.14 Maira has a total of ` 1040 as currency notes in the denomination of ` 10, ` 20 and ` 50. The ratio of

the number of ` 10 notes and ` 20 notes is 2:5. If she has a total of 30 notes, how many notes of each

denomination she has.​

Answer 1

Step-by-step explanation:

ANSWER:-

Given that:-

• Total sum of money she has is 1040.
• Denominations are 10, 20 and 50.
• 10 and 20 notes are in ratio 2: 5

To find:-

• Number of notes in each domination, Maira has.
• Concept- Ratio and Proportion

Let's Do!

So, let us start with the ratio constant x. So, we can state that the ratio of 10 and 20 notes are 2x and 5x respectively.

So, we can state for time being:-

Let the 50 notes be y.

So,

$\rm{2x+5x + y = 30}$ - Given

$\rm{7x + y = 30}$

$\rm{y = 30 - 7x}$ ------------(1)

Now, according to question:-

$\rm{10(2x) + 20(5x) + 50(30 - 7x) = 1040}$

Using distributive property,

$\rm{ 20x + 100x + 1500 - 350x = 1040}$

$\rm{ 120x + 1500 - 350x = 1040}$

$\rm{ 120x + 1500 - 350x = 1040}$

$\rm{ - 230x = 1040 - 1500 }$

$\rm{ - 230x = - 460 }$

$\rm{ x = \dfrac{460}{230} }$

$\boxed{\rm{ x = 2 }}$

Now, placing the values of x:-

$\sf{ 2x = 2 \times 2 = 4 \ notes }$

$\sf{ 5x = 5 \times 2 = 10 \ notes }$

$\sf{ 30 - 7x = 30 - (7 \times 2) = 30 - 14 = 16 \ notes }$

So, 4 notes, 10 notes and 16 notes respectively is the required answer.

Answer 2

Answer:

Given

• Total sum of money she has is 1040.
• Denominations are 10, 20 and 50.
• 10 and 20 notes are in ratio 2: 5

To Find :-

Total notes of dimensions

Solution :-

Let the 10 rupee note be 2x, 20 rupee note 5x and 50 rupee note be y

2x+5x+y=30

7x+y=30

y=30−7x ------------(1)

20x+100x+1500−350x=1040

120x+1500−350x=1040

120x+1500−350x=1040

−230x=1040−1500

−230x=−460

$\tt \: x = \frac{ - 460}{ - 230}$

x = 2

10 rupee note 14 notes,

5 rupee note 10 note

50 rupee note 16 notes