Question

in a lottery there are prizes of rs 100 and rs 500.if the total number of prizes are 200 and the total prize money is rs 50,000, find the number of each prize?

Answer 1

Let no. of Rs. 100 prizes be x.
∴ No. of Rs. 500 prizes = (200-x)

Cost of all Rs. 100 prizes = Rs. 100x
Cost of all Rs. 500 prizes = 500(200-x) = Rs. (100000-500x)
As per question,

50000 = (100000-500x)+100x
=> 500x-100x = 100000-50000
=> 400x = 50000
=> x = 500/4 = 125

No. of Rs. 100 prizes = 125
No. of Rs. 500 prizes = 200-125 = 75

Answer 2

Answer:

No. of Rs. 100 prizes is 125 and No. of Rs. 500 prizes is  75

Step-by-step explanation:

Let no. of Rs. 100 prizes be x.

Since we are given that  the total number of prizes are 200

So, no. of 500 prizes = 200-x

Cost of all Rs. 100 prizes = Rs. 100x

Cost of all Rs. 500 prizes = 500(200-x) = Rs. (100000-500x)

Now we are given that the total prize money is rs 50,000,

So, $50000 =(100000-500x)+100x$

=>$500x-100x = 100000-50000$

=> $400x = 50000$

=> $x = \frac{50000}{400}$

=> x =125

No. of Rs. 100 prizes = 125

No. of Rs. 500 prizes = 200-125 = 75

Hence No. of Rs. 100 prizes is 125 and No. of Rs. 500 prizes is  75