Question

- Raj has a sum of 2 800 in the form of denominations of 10 and 20. If the total number
of notes be 50, find the number of notes of each type.​

Answer 1

Correct Question :-

Raj has a sum of Rs. 800 in the form of denominations of Rs. 10 and Rs. 20. If the total number of notes be 50, find the number of notes of each type.

Answer :-

Number Rs. 10 notes and Rs. 20 notes are 20 and 30 respectively.

Explanation :-

Let the number of Rs. 10 notes be x

Total number of notes = 50

So, Number of Rs. 20 notes = 50 - x

Value of Rs. 10 notes = 10 * Number of Rs.10 notes = Rs. 10x

Value of Rs. 20 notes = 20 * Number of Rs. 20 notes = 20(50 - x) = Rs. (1000 - 20x)

Given

Total value of money = Rs. 800

⇒ Value of Rs. 10 notes + Value Rs. 20 notes = Rs. 800

⇒ 10x + (1000 - 20x) = 800

⇒ 10x + 1000 - 20x = 800

⇒ - 10x + 1000 = 800

⇒ 1000 - 800 = 10x

⇒ 200 = 10x

⇒ 200/10 = x

⇒ 20 = x

⇒ x = 20

i.e Number of Rs. 10 notes = x = 20

Number of Rs. 20 notes = (50 - x) = (50 - 20) = 30

Therefore the number Rs. 10 notes and Rs. 20 notes are 20 and 30 respectively.

Answer 2

Correct Question:

- Raj has a sum of ₹ 800 in the form of denominations of ₹ 10 and ₹ 20. If the total number of notes be 50, find the number of notes of each type.

Answer:

Rs.10 notes are 20 in number and Rs. 20 notes are 30 in number.

Step-by-step explanation:

Given :

Amount = Rs. 800

In denominations of = Rs. 10 and Rs. 20.

Total notes = 50

To find :

Notes of each type

Solution :

$\textbf{\small{\underline{Let the number of - }}}$

• Rs. 10 notes be y
• Rs. 20 notes be (50 - y)

→ Rs. 10 notes = y

→ Their value = 10(y)

→ Rs. 20 notes = (50 - y)

→ Thier value = 20(50 - y)

$\rule{300}{1.5}$

★$\green{\boxed{\green{\boxed{\red{\sf{10(y)+20(50-y)=800}}}}}}$

$\sf{\implies} \: 10(y)+20(50-y)=800 \\ \sf{\implies} \:10y + 1000 - 20y = 800 \\ \sf{\implies} \:10y - 20y = 800 - 1000 \\ \sf{\implies} \:\cancel - 10y = \cancel - 200 \\ \sf{\implies} \:y = \frac{200}{10} \\ \sf{\implies} \:y = 20$

Number of Rs. 10 notes = 20

$\rule{300}{1.5}$

★ Value of (50 - y)

$\sf{\implies} \:50 - 20 \\ \sf{\implies} \:30$

Number of Rs. 20 notes = 30

$\therefore$ Rs.10 notes are 20 in number and Rs. 20 notes are 30 in number.