Question

in a lottery a total of 250 prizes are given. the prize is given in the denomination of rupees 500 and 1000 notes. if the total prize money is 180000 find the number of notes.

Answer 1

LET THE NO. 500 NOTE BE X

AND NO. OF 1000 NOTES BE Y

THEN,

TOTAL PRIZES = 250

SO,

X + Y = 250 ___ (1)

ACCORDING TO QUESTION,

SUM OF ₹ OF 500 NOTES = 500X

AND

SUM OF ₹ OF 1000 NOTES = 1000Y

TOTAL PRIZE = 180000

SO,

500X + 1000Y = 180000

500(X+2Y) = 180000

X + 2Y = 360

X + 2Y - 110 = 250 ___ (2)

EQUALISING EQUATION (1) & (2)

X + 2Y - 110 = X + Y

2Y - 110 = Y

Y = 110

NOW,

PUTTING THE VALUE OF Y IN EQUATION (1)

X + 110 = 250

X = 140

WE CAN SAY THAT TOTAL NO. OF ₹ 500 NOTES ARE 140

AND

TOTAL NO. OF ₹ 1000 NOTES ARE 110.

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