A man buys 2pens and 4 pencils and gives a hundred rupees note to shop keeper . Shopkeeper ask him to pay Rs10 more to take 4pens and 2pencils. If he bought 2pens and 3pencils how much would the man get back from shopkeeper?
Good
Very bad answer
Well, it looks like the shopkeeper is trying to play some mathematical tricks with the poor man! Let's crunch the numbers and find out how much he would get back.
Let's assume the cost of each pen is P rupees and each pencil is C rupees. According to the information given, we can form two equations:
2P + 4C = 100 (Equation 1)
4P + 2C + 10 = 100 (Equation 2)
Now, let's solve these equations to find the values of P and C.
From Equation 1, we get:
2P + 4C = 100
Dividing by 2 on both sides, we have:
P + 2C = 50 (Equation 3)
From Equation 2, we get:
4P + 2C + 10 = 100
Simplifying, we get:
4P + 2C = 90 (Equation 4)
Now, let's subtract Equation 3 from Equation 4 to get the value of P:
4P + 2C - (P + 2C) = 90 - 50
3P = 40
P = 40/3
Now, substituting the value of P in Equation 3:
(40/3) + 2C = 50
Multiplying both sides by 3 to get rid of the fraction:
40 + 6C = 150
6C = 150 - 40
6C = 110
C = 110/6
So, the cost of each pen (P) is approximately 13.33 rupees, and the cost of each pencil (C) is approximately 18.33 rupees.
Now if the man bought 2 pens and 3 pencils, the total cost would be:
2P + 3C = 2(13.33) + 3(18.33) = 26.66 + 54.99 = 81.65
Since he gave a hundred rupees note to the shopkeeper, he would get back:
100 - 81.65 = 18.35 rupees.
So, the man would get approximately 18.35 rupees back from the shopkeeper. I hope that puts a smile on your face!
To solve this problem, we need to determine the total cost of 2 pens and 4 pencils and then compare it with the cost of 4 pens and 2 pencils.
Let's assume the cost of one pen is x and the cost of one pencil is y.
The total cost of 2 pens and 4 pencils can be calculated as follows:
2x (cost of 2 pens) + 4y (cost of 4 pencils) = 100 (rupees)
The shopkeeper asks for an additional Rs10 to give 4 pens and 2 pencils. So, the total cost of 4 pens and 2 pencils is:
4x (cost of 4 pens) + 2y (cost of 2 pencils) = 100 + 10 = 110 (rupees)
Now, we have a system of two equations:
2x + 4y = 100 ---(1)
4x + 2y = 110 ---(2)
We can solve these equations simultaneously to find the values of x and y.
Multiplying equation (1) by 2 and equation (2) by 4, we have:
4x + 8y = 200 ---(3)
4x + 2y = 110 ---(4)
By subtracting equation (4) from equation (3), we can eliminate the x variable:
(4x + 8y) - (4x + 2y) = 200 - 110
6y = 90
y = 90/6
y = 15
Substituting the value of y in equation (1), we can find the value of x:
2x + 4(15) = 100
2x + 60 = 100
2x = 100 - 60
2x = 40
x = 40/2
x = 20
So, the cost of one pen is Rs20 and the cost of one pencil is Rs15.
Now, the man wants to buy 2 pens and 3 pencils. We can calculate the total cost by:
2x (cost of 2 pens) + 3y (cost of 3 pencils) = 2(20) + 3(15) = 40 + 45 = 85
The man gave a hundred rupee note to the shopkeeper. So, he would get back:
Change = 100 - 85 = 15 rupees
Therefore, the man would get Rs15 as change from the shopkeeper.
cost of a pen --- x
cost of a pencil -- y
2x + 4y ≤ 100
4x + 2y = (2x+4y) + 10
2x - 2y = 10
x-y= 5
x = 5+y
then back in 2x+4y<100
or x+2y ≤ 50
5+y + 2y ≤ 50
3y ≤ 45
y ≤ 15
cost of 2 pens and 3 pencils
= 2x + 3y
= 2(5+y) + 3y
= 10 + 5y
there are multiple answers
Make a chart showing
x .. y (2x+4y) (4x+2y) (2x+3y)
20 15 -- 100 -- 110 -- 85 , so change is 15
19 18 -- 94 --- 104 -- 80 , so change is 20
etc.
(If we assume that Rs 100 was the exact amount for 2pens and 4 pencils, then
20, 15 is the correct answer.)
e.g.
If he bought 2 pens at 20 and 4 pencils at 15
cost would be 100
Had he bought 4 pens and 2 pencils, cost would be 110 which is 10 more as stated,
so cost of 2 pens and 3 pencils is 85, resulting in change of 15
the same can be done for each of the entries in the chart.
Good but I don't want on graph only solution
Let the cost of a pen and a pencil be x and y respectively.
4x+4y=100
x+y=25 ...(1)
3x=y+15
3x−y=15 ...(2)
Adding (1) and (2), we get
4x=40
x=10
Substitute x=10 in equation (1) to get y=15.