(6) Durga’s mother gave some 10 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 ?



Sol. Let the no. of Rs. 10 notes given to Durga be x and the no. of Rs.5 notes given to her be y.
As per the first condition,
10x + 5y = 190 ....... eq. no. (1)
As per the second condition,
5x + 10y = 185 ......eq. no. (2)
Adding (1) and (2),
10x + 5y = 190
5x + 10y = 185
15x + 15y = 375
∴ 15(x + y) = 375
∴ x + y = 375/15
∴  x + y = 25 ......(3)
Subtracting (2) from (1),
10x + 5y = 190
5x + 10y = 185
(-)   (-)       (-)
5x – 5y = 5
∴ 5(x – y) = 5
∴ x – y = 5/5
∴ x – y = 1 .......(4)
Adding (3) and (4),
x + y = 25
x – y = 1
2x    = 26
∴ x = 26/2
∴ x = 13
Substituting x = 13 in eq. no. (3)
∴ x + y = 25
∴ 13 + y = 25
∴ y = 25 – 13
∴ y = 12

Durga had 13 notes of Rs. 10 and 12 notes of Rs. 5.

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