Lakshmi is a cashier in a bank. She has currency notes of denominations ₹100,₹50 and ₹10 respectively. The ratio of the number of these notes 2:3:5. The total cash with Lakshmi is ₹4,00,000. How many notes of each denomination does she have ? Give answer in full statement.
Answers
Step-by-step explanation:
Given :-
Lakshmi is a cashier in a bank. She has currency notes of denominations ₹100,₹50 and ₹10 respectively. The ratio of the number of these notes 2:3:5. The total cash with Lakshmi is ₹4,00,000.
To find :-
How many notes of each denomination does she have ?
Solution :-
Given that
Lakshmi is a cashier in a bank. She has currency notes of denominations ₹100,₹50 and ₹10 respectively.
The ratio of the number of these notes = 2:3:5
Let the number of ₹ 100 notes be 2X
The value of 2X ,₹ 100 notes
= ₹ 100 ×2X
= ₹ 200X
Let the number of ₹ 50 notes be 3X
The value of 3X ,₹ 50 notes
= ₹ 50× 3X
= ₹ 150X
Let the number of ₹ 10 notes be 5X
The value of 5X, ₹ 10 notes
= ₹ 10 × 5X
= ₹ 50X
Total amount with Lakshmi
= 200X + 150X +50X
= ₹ 400X
According to the given problem
The total cash with Lakshmi = ₹4,00,000
=> 400 X = 400000
=> X = 400000/400
=> X = 1000
Now,
The number of ₹ 100 notes = 2X
=> 2×1000 = 2000
The number of ₹ 50 notes = 3X
=> 3×1000 = 3000
The number of ₹ 10 notes = 5X
=> 5×1000 = 5000
Answer:-
The number of ₹ 100 notes = 2000
The number of ₹ 50 notes = 3000
The number of ₹ 10 notes = 5000
Check:-
The ratio of all notes
= 2000:3000:5000
= 2:3:5
The number of ₹ 100 notes = 2000
Value of that notes = 2000×100
= ₹ 200000
The number of ₹ 50 notes = 3000
Value of that notes = 3000×50
= ₹ 150000
The number of ₹ 10 notes = 5000
Value of that notes = 5000×10
= ₹ 50000
Total money with Lakshmi
= 2,00,000+1,50,000+50,000
= ₹4,00,000
Verified the given relations in the given problem.