Amit and Bilal buy goods for ₹1,500 and ₹2,000, respectively. Amit marks his goods up by y%, while Bilal marks his goods up by 2y% and offers a discount of y%. If both make the same profit, then find the value of y.

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Let the cost price (CP) of Amit's goods be ₹1500 and Bilal's goods be ₹2000.

Amit's selling price (SP_A) = CP_A + profit = 1500 + (y% of 1500) = 1500 * (1 + y/100)

Bilal marks up his goods by 2y%, so the marked price (MP_B) = 2000 * (1 + 2y/100)

Bilal offers a discount of y%, so his selling price (SP_B) = MP_B * (1 - y/100) = 2000 * (1 + 2y/100) * (1 - y/100)

Both make the same profit, so:
SP_A - CP_A = SP_B - CP_B

Substitute values:
1500 * (1 + y/100) - 1500 = 2000 * (1 + 2y/100) * (1 - y/100) - 2000

Simplify left side:
1500 * y/100 = 2000 * [(1 + 2y/100)(1 - y/100)] - 2000

Calculate the expression inside the bracket:
(1 + 2y/100)(1 - y/100) = 1 + 2y/100 - y/100 - (2y^2)/(10000) = 1 + (y/100) - (2y^2)/10000

So,
1500 * y/100 = 2000 * [1 + (y/100) - (2y^2)/10000] - 2000

Simplify right side:
= 2000 + 2000 * (y/100) - 2000 * (2y^2/10000) - 2000

= 2000 * (y/100) - 2000 * (2y^2/10000)

= 20y - (2000 * 2y^2)/10000 = 20y - (4000y^2)/10000 = 20y - 0.4y^2

Now equate both sides:
1500 * y/100 = 20y - 0.4y^2

Simplify left side:
15y = 20y - 0.4y^2

Bring all terms to one side:
0.4y^2 - 5y = 0

Divide by y (y ≠ 0):
0.4y - 5 = 0

0.4y = 5

y = 5 / 0.4 = 12.5

Therefore, the value of y is 12.5%.

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