(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.