Question

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.

Answer 1

$Solution :$

The ratio of the notes is :  2 : 3 : 5

Let her have    2 * N number of Rs 100 notes,    3 * N number of Rs 50 notes,  and 5 * N  number of Rs 10 notes respectively.

Then the total value of the currency notes will be:

     2 N * Rs 100 + 3 N * Rs 50 + 5 N * Rs 10  =  Rs 4, 00, 000

 =>    200 N + 150 N + 50 N = Rs 4, 00, 000

 =>    400 N = Rs 4, 00, 000

     =>  N = 1, 000

   

Hence,  There are 2N = 2,000 notes of Rs 100  ,   3N = 3,000 notes of Rs 50 and  finally ,  5 N = 5, 000 notes of Rs 10..

Answer 2

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$\LARGE\mathfrak{\underline\textcolor{aqua}{✯\; Given :-}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Currency notes of denominations = ₹ 100 , ₹ 50 , ₹ 10 .}$

$\qquad\tt{:}\longrightarrow\large\textsf{The Ratio of the number of notes = 2 : 3 : 5}$

$\qquad\tt{:}\longrightarrow\large\textsf{Total cash with Lakshmi = ₹ 400000 .}$

$\large\textsf{ }$

$\LARGE\mathfrak{\underline\textcolor{aqua}{✯\; To \; \; Find :-}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Number of notes of each denomination = ?}$

$\large\textsf{ }$

$\LARGE\mathfrak{\underline\textcolor{aqua}{✯\; Solution :-}}$

$\large\textsf{ }$

↝ Assume the common multiple of the number of the notes of the given denominations as ' x ' . So the ratio would be ' 2x : 3x : 5x ' . Now we know that she has a total cash of ' Rs. 400000 ' . We know that we have total ' 2x ' notes of ' ₹ 100 ' so the total amount made by the number of ₹ 100 notes will be ' ₹ 200x ' . Similarly the total amount made by the number of ₹ 50 notes will be ' ₹ 150x ' and the total amount made by the number of ₹ 10 notes will be ' ₹ 50x ' . So now we add all this total amount to get the value of ' x ' and once we get the value of ' x ' we can find the total number of notes of each denomination .

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{200x + 150x + 50x = 400000}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{400x = 400000}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{x = \cfrac{\large\textsf{400000}}{\large\textsf{400}} }\\\\\\\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{x = 1000}}\\\\\\\boxed{\large\textsf\textcolor{orange}{∴ The value of x = 1000}}$

$\large\textsf{ }$

∴ The total number of notes of ₹ 100 = 2 × 1000 = 2000

∴ The total number of notes of ₹ 50 = 3 × 1000 = 3000

∴ The total number of notes of ₹ 10 = 5 × 1000 = 5000

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