Question

Q. 14. Lakshmi is a cashier in a bank.
She has currency notes of denominations
Rs. 100, Rs. 50 and Rs. 10, respectively. The
ratio of the number of these notes is 2:3:5.
The total cash with Lakshmi is Rs. 4,00,000.
How many notes of each denomination does
she have?​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Laxmi has 2000 notes of Rs. 100 notes, 3000 notes of Rs. 50 and 5000 notes of Rs. 10.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Total cash with Laxmi = Rs. 4,00,000

Ratio of Rs. 100, Rs. 50 and Rs. 10 notes = 2 : 3 : 5

To Find :

Notes of each denomination with Laxmi

Solution :

◆ $\textbf{\small{\underline{Consider -}}}$

• Number of Rs. 100 notes as 2x
• Number of Rs. 50 notes as 3x
• Number of Rs. 10 notes as 5x

$\boxed{\sf{100(2x)+50(3x)+10(5x)=4,00,000}}$

$\tt{\longrightarrow} \: 100(2x)+50(3x)+10(5x)=400000$

$\tt{\longrightarrow} \: 200x+150x+50x=400000$

$\tt{\longrightarrow} \: 200x+200x=400000$

$\tt{\longrightarrow} \: 400x=400000$

$\tt{\longrightarrow} \:x = \dfrac{400000}{400}$

$\tt{\longrightarrow} \:x = 100$

$\rule{300}{1.5}$

★ Value of 2x

$\tt{\longrightarrow} \:2 \times 1000$

$\tt{\longrightarrow} \:2000$

Rs. 100 notes = 2000

$\rule{300}{1.5}$

★ Value of 3x

$\tt{\longrightarrow} \:3 \times 1000$

$\tt{\longrightarrow} \:3000$

Rs. 50 notes = 3000

$\rule{300}{1.5}$

★ Value of 5x

$\tt{\longrightarrow} \:5 \times 1000$

$\tt{\longrightarrow} \:5000$

Rs. 10 notes = 5000

$\therefore$ Laxmi has 2000 notes of Rs. 100 notes, 3000 notes of Rs. 50 and 5000 notes of Rs. 10.

Answer 2

Answer -

let Rs. 100, Rs. 50 and Rs. 10 as 2x, 3x and 5x respectively.

==> 100(2x) + 3x(50) + 5x(10) = 4,00,000

==> 200x + 150x + 50x = 4,00,000

==> 400x = 400000

==> x = 400000/400

==> x = 1000

Rs. 100 = 1000 × 2 = 2000

Rs. 50 = 1000 × 3 = 3000

Rs. 10 = 1000 × 5 = 5000

Laxmi has 2000 notes of Rs. 100 notes, 3000 notes of Rs. 50 and 5000 notes of Rs. 10.