Discussion
A bill for Rs. 1840 is paid with denominations of Rs. 50, Rs. 20 and Rs. 10 notes. 50 notes are used in all, and the number of Rs. 50 notes is 6 more than the number of Rs. 20 notes. Find the number of Rs. 50 notes.
Answer: C
Let x, y, and z be the number of notes of Rs. 50, Rs. 20, and Rs. 10 respectively.
Equation 1 (Total notes): x + y + z = 50
Equation 2 (Total value): 50x + 20y + 10z = 1840
Equation 3 (Constraint): x = y + 6
Substitute (3) into (1): (y+6) + y + z = 50 => 2y + z = 44 => z = 44 - 2y.
Now substitute x and z into (2):
50(y+6) + 20y + 10(44-2y) = 1840
50y + 300 + 20y + 440 - 20y = 1840
50y + 740 = 1840
50y = 1100 => y = 22.
Now find x: x = y + 6 = 22 + 6 = 28.
The number of Rs. 50 notes is 28.
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