Question

A man had a table to sell. I offered him a sum of moneyfor the table which he refused as being 13% below thevalue of the table. I offered then Rs. 450 more andthe second offer was 5% more than the estimated value.Find the value of the table.​

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, The value of table is Rs.x .

So,

→ my offered money = 13% below to Rs.x

Or,

→ my offered money = 87% of Rs.x = Rs.(87x/100)

Now, if I offered Rs. 450 more it was 5% more than the estimated value.

So,

→ (87x/100) + 450 = 5% more than Rs.x

→ (87x/100) + 450 = 105% of Rs.x

→ (87x/100) + 450 = (105x/100)

→ (105x/100) - (87x/100) = 450

→ (105x - 87x) /100 = 450

→ 18x/100 = 450

→ 18x = 450 * 100

→ 2x = 50 * 100

→ x = 25 * 100

→ x = Rs.2500 (Ans.)

Hence, The value of Table is Rs.2500.

Answer 2

Let the price of table be x.

And let the money offered intially be P

Then, According To Question the initial money offered is 13% less,

Therefore,

$\sf{ \implies x - 13\% \: of \: x = p} \\ \\ \sf{ \implies x = \frac{13}{100} \times x = p } \\ \\ \sf{ \implies 0.87x = p \: - - - - (1)}$

And then the second offering is 450 more than and it is 5% more than the actual price.

Hence,

$\sf{First \: offering + 450 = x + 5\% \: of \: x} \\ \\ \sf{ \implies 0.87x + 450 = x + \frac{5}{100} \times x } \: \: \: \: [from \: equ \: (1)] \\ \\ \sf{ \implies 450 = 1.05x - 0.57x} \\ \\ \sf{ \implies 450 = 0.18x} \\ \\ \sf {\purple{ \implies \underline{\boxed{ \sf{x = 2500}}}}}$

$\sf{\purple{\therefore\: Hence, \:the\: value \:of \:table = Rs.\:2500}}$