Durga’s mother gave some ten Rupee notes and some 5 rupee notes to her, which amounts to Rs. 190. Durga said, ‘if the number of 10 rupee notes and 5 rupee
notes would have been interchanged, I would have Rs. 185 in my hand.’
So how many notes of rupee 10 and rupee 5 were given to Durga?
(Q)
Sol.
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Rs. 10 note
Rs. 5 note
No. of notes
x
y
= Amount
No. of notes
×
Denomination
= 20
2
×
10
= 40
4
×
10
= 10x
x
×
10
Amount
10x
5y
190
Total
10y
5x
185
Let the number of notes of Rs. 10 be x and number of notes of Rs. 5 be y
The amount will be
There are two types of notes
Rs. 5 Note
Rs. 10 Note
Since we don’t know the how many Rs. 10 and Rs. 5 notes were given to Durga
Let us assume
We have to find the number of notes of each types
Let us take an example
If there are two notes of rupees 10
If there are four notes of rupees 10
The amount will be
For Rs. 10 notes amount will be
There are y notes of Rs. 5
There are x notes of Rs. 10
And the total amount is given as
So here we can conclude
So if there are x notes of Rs. 10
For Rs. 5 notes amount will be
And the total amount is given as
The amount will be
The amount will be
As per the 1st given condition,
10x
+
5y
= 190
Dividing throughout by 5, we get
2x
+
y
= 38
........(i)
As per the 2nd given condition,
5x
+
10y
= 185
Dividing throughout by 5, we get
x
+
2y
= 37
........(ii)
How many types of notes are there
What do we have to find?
Let us understand the sum with the help of a table
Durga’s mother gave some ten Rupee notes and some 5 rupee notes to her, which amounts to Rs. 190. Durga said, ‘if the number of 10 rupee notes and 5 rupee
notes would have been interchanged, I would have Rs. 185 in my hand.’
So how many notes of rupee 10 and rupee 5 were given to Durga?
(Q)
As per the 1st given condition,
2x
+
y
= 38
........(i)
As per the 2nd given condition,
x
+
2y
= 37
........(ii)
Multiplying (ii) by 2, we get
Durga has 13 notes of Rs.10 and 12 notes of Rs.5
Sol.
Let the number of notes of Rs. 10 be x and number of notes of Rs. 5 be y
2x
+
4y
= 74
........(iii)
Subtracting (i) from (iii),
2x + 4y = 74
2x + y = 38
3y
(–) (–) (–)
= 36
∴ y = 12
Substituting y = 12 in (ii),
x
+ 2(12)
= 37
x
+ 24
= 37
∴
x
=
∴
x
= 13
37
–
24