A boy buys 18 sharpeners, (Brown/white) for Rs.100. For every white sharpener,…

Let the price of a brown sharpener be x rupees and the price of a white sharpener be x + 1 rupees.

Let the number of white sharpeners be w and the number of brown sharpeners be b. Then

b + w = 18

Total cost: w(x + 1) + b·x = 100

Substitute b = 18 − w into the cost equation:

w(x + 1) + (18 − w)x = 100

This simplifies to w + 18x = 100, so w = 100 − 18x.

• Try integer values for x (price of a brown sharpener). For x = 5, w = 100 − 18×5 = 10. Then white price = x + 1 = 6 and brown count = 18 − 10 = 8. Check: 10×6 + 8×5 = 60 + 40 = 100, which works.

• Other integer x values give w outside the valid range 0–18 (for example x = 4 gives w = 28, x = 6 gives w = −8), so x = 5 is the only feasible integer solution.

Therefore the white sharpener costs Rs.6 and he bought 10 white sharpeners.