5. The total cash with Lakshmi is ₹4,00,000. How many notes of each denomination does she have?

Let the numbers of notes of ₹100, ₹50 and ₹10 be $2x$, $3x$ and $5x$, respectively.

Value of ₹100 notes = $2x \times 100 = 200x$  
Value of ₹50 notes = $3x \times 50 = 150x$  
Value of ₹10 notes = $5x \times 10 = 50x$  

According to the question:

$200x + 150x + 50x = 400000$
$\Rightarrow 400x = 400000$
$\Rightarrow x = \dfrac{400000}{400}$
$\Rightarrow x = 1000$

Numbers of ₹100 notes = $2x = 2000$  
Numbers of ₹50 notes = $3x = 3000$  
Numbers of ₹10 notes = $5x = 5000$

मान लीजिए ₹100, ₹50 और ₹10 के नोटों की संख्या $2x$, $3x$ और $5x$ है।  

₹100 के नोटों का मूल्य = $2x \times 100 = 200x$  
₹50 के नोटों का मूल्य = $3x \times 50 = 150x$  
₹10 के नोटों का मूल्य = $5x \times 10 = 50x$  

प्रश्न के अनुसार:

$200x + 150x + 50x = 400000$
$\Rightarrow 400x = 400000$
$\Rightarrow x = \dfrac{400000}{400}$
$\Rightarrow x = 1000$

₹100 के नोटों की संख्या = $2x = 2000$  
₹50 के नोटों की संख्या = $3x = 3000$  
₹10 के नोटों की संख्या = $5x = 5000$