Question

a boy buys 18 sharpeners (brown or white) for rs. 100. for every white sharpener he pays one rupee more than the brown sharpener. what is the cost of white sharpener & how much did he buy?

Answer 1

Total sharpeners purchased

Let the number of white sharpeners be x

So the number of brown sharpeners = 18-x

Let the cost of brown sharpener = z

So the cost of white sharpener = z+1

Total cost = 100

x(z+1) + (18-x)(z) = 100

xz + x + 18z-xz = 100

18z + x =100

18z = 100-x

Now as the value of x needs to be 18(total sharpeners)

And the multiple of 18 close to 100 is 90

So if x = 10

18z = 100-10

18z = 90

z= 5

The cost of white sharpeners shall be = z + 1 = 5 + 1 = Rs 6

So he bought 10 white sharpeners at Rs 6 each.

He also bought 8 brown sharpeners at Rs 5 each.

Answer 2

Answer:

Total sharpeners purchased 18

Let the number of white sharpeners be s.

So the number of brown sharpener 18-s

Let the cost of brown sharpener be x

so the cost of white sharpener x+1

total cost of sharpeners =rupees 100

s(x+1)+(18-s)(x)=100

x ×5+18-x×x=100

18x+s =100

18x =100 - s

Now the value of s needs to be 18

And the multiple of 18 close to 100 is only 90 so

so s = 18 = 100 - 10

s= 18 = 90

s = 5

The cost of white sharpener is 6.