Question

A total of ₹10000 is distributed among 150 persons as gift. A gift is either of ₹50 or ₹100. Find the number of gifts of each type.

Answer 1

Step-by-step explanation:

Given :A total of rs 10000 is distributed among 150 persons as a gift. a gift is either of rs 50 or rs 100.

To Find : Find the no of each type of note.

Solution:

let x be the number of Rs.50 prizes

let y be the number of Rs.100 prizes

Since we are given that the prizes are distributed among 150 persons

So, x+y=150x+y=150 ------1

Now we are given that A total of rs 10000 is distributed

So, 50x+100y=1000050x+100y=10000 ---2

Substitute the value of x from 1 in 2

50(150-y)+100y=1000050(150−y)+100y=10000

7500-50y+100y=100007500−50y+100y=10000

7500+50y=100007500+50y=10000

50y=10000-750050y=10000−7500

50y=250050y=2500

y=\frac{2500}{50}y=

50

2500

y=50y=50

Substitute the value of y in 1 to get value of x

x+50=150x+50=150

x=100x=100

Hence the number of Rs.50 prizes is 100 and the number of Rs.100 prizes is 50

Answer 2

Answer:

50x+100y=10000

x+2y=200------>1

x+y=150--------->2

On solving 1 and 2

x=100 , y =50

Therefore the number of gifts of each type is 100 and 50 respectively