Question

Nitish sold his watch and sun glasses at a loss of 4% and gain of 4% respectively
for 2600 to Kamal. Kamal sold the same sun glasses and watch at a loss of 4%
and gain of 4% respectively for 2700. The price of watch and sun glasses to
Nitish were.​

Answer 1

Given:

Nitish sold his watch and sunglasses at a loss of 4% and gain of 4% respectively  for 2600 to Kamal.

Kamal sold the same sunglasses and watch at a loss of 4%  and gain of 4% respectively for 2700.

To find:

The price of the watch and sunglasses to  Nitish was?​

Solution:

Formula to be used:

$\boxed{\bold{S.P. = \frac{100 + G\%}{100}\times C.P. }}\\\\\boxed{\bold{S.P. = \frac{100 - L\%}{100}\times C.P. }}$

Let's assume,

"x" → represents the cost price of the watch

"y" → represents the cost price of the sunglasses

According to the transaction between Nitish and Kamal, we can form an equation as:

$\frac{100 -4 }{100} \times x \:+\: \frac{100 + 4 }{100} \times y = 2600$

$\implies \frac{96 }{100} \times x \:+\: \frac{104 }{100} \times y = 2600$

$\implies 0.96 x \:+\: 1.04 y = 2600$ ....... (i)

According to the transaction done by Kamal, we can form an equation as:

$\frac{100 +4 }{100} \times x \:+\: \frac{100 - 4 }{100} \times y = 2700$

$\implies \frac{104 }{100} \times x \:+\: \frac{96 }{100} \times y = 2700$

$\implies 1.04 x \:+\: 0.96 y = 2700$ ....... (ii)

On multiplying eq. (i) by 1.04, we get

$\implies 0.9984x \:+\: 1.0816 y = 2704$ ..... (iii)

On multiplying eq. (ii) by 0.96, we get

$\implies 0.9984x \:+\: 0.9216y = 2592$ ..... (iv)

On subtracting eq. (iii) & (iv), we get

0.9984x + 1.0816y = 2704

0.9984x + 0.9216y = 2592

-              -                  -

-----------------------------------------

         0.16y = 112

-----------------------------------------

∴ y = $\frac{112}{0.16} = \bold{700}$

On substituting the value of y in eq. (i), we get

0.96x + (1.04 × 700) = 2600

⇒ 0.96x + 728 = 2600

⇒ 0.96x = 2600 - 728

⇒ 0.96x = 1872

⇒ x = $\frac{1872}{0.96}$

⇒ x = 1950

Thus,

The price of the watch to Nitish was Rs. 1950.

and

The price of sunglasses to Nitish was Rs. 700.

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Answer 2

Answer:

the ans is (Rs.1950,Rs.700)