Question

a man purchased two lines for 2030 by selling once table lamp at the profit 6% and other at the loss of 10% in either guns for nerves on this transaction find the cost price is a table lamp

Answer 1

it seems mistakes in question. let us assume that s.p of each table is same .

then solution:
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c.p of two lamps = 2030

let c.p of 1st lamp = x

c.p of 2nd lamp = 2030 - x

s.p of 1st lamp = x + 6% of x

= ₹1.06x

s.p of 2nd lamp = (2030 - x) - 10%of (2030 -x)

= 2030 - x - 203 + 0.1x

= 1827 - 0.9x

s.p of 1st lamp = s.p of 2nd lamp

1.06x = 1827 - 0.9x

1.06x + 0.9x = 1827

1.96x = 1827

x = ₹932.15

c.p of first lamp = 932.15

c.p of second lamp = 2030 - x

= 2030 - 932.15 = ₹1097.85

Answer 2

SP = 2030
loss= 10% - 6% = 4 %

CP = 2030 4%
= 2030 1% = 2030/100 = 20.30
=4% = 20.30 × 4= 81.20
2030 + 81.20 = 2110.20

price = 2110.20 ÷ 2= 1050.10