Math, asked by keshavsundas, 18 hours ago

3) Niruta sold two washing machines for Rs 9900 each. She sold one at a gain of 10% and the other at a loss of 10%. Find her gain or loss % in the whole transaction.​

Answers

Answered by PopularStar
8

Given:

Niruta sold two washing machines for Rs.9900 each.He sold one at a gain of 10% & other at a loss of 10%.

Find:

Profit or Loss..

Solution:

 \underline{\bf{Explanation\::}}

 \underbrace{\sf{1^{st}\:Case\::}}

Selling price of first washing machine, (S.P) = Rs.9900

Gain on washing machine = 10%

C.P = ?

Using formula of the cost price when become profit;

 \boxed{\bf{Cost \ price = \bigg(\frac{100}{100+profit}\bigg) \times S.P}}

So,

 \mapsto\tt{Cost\:price = \bigg(\dfrac{100}{100+profit} \bigg) \times S.P}

 \mapsto\tt{Cost\:price = \bigg(\dfrac{100}{100+10} \bigg) \times 9900}

 \mapsto\tt{Cost\:price = \bigg(\dfrac{100}{110} \bigg) \times 9900}

 \mapsto\tt{Cost\:price = \dfrac{100}{\cancel{110}} \times \cancel{9900}}

 \mapsto\tt{Cost\:price = Rs.(100 \times 90)}

 \mapsto\bf{Cost\:price = Rs.9000}

 \underbrace{\sf{2^{nd}\:Case\::}}

Selling price of second washing machine, (S.P) = Rs.9900

Loss on washing machine = 10%

C.P = ?

Using formula of the cost price when become loss;

 \boxed{\bf{Cost\:price = \bigg(\frac{100}{100-loss}\bigg) \times S.P}}

So,

 \mapsto\tt{Cost\:price = \bigg(\dfrac{100}{100-loss} \bigg) \times S.P}

 \mapsto\tt{Cost\:price = \bigg(\dfrac{100}{100-10} \bigg) \times 9900}

 \mapsto\tt{Cost\:price = \bigg(\dfrac{100}{90} \bigg) \times 9900}

 \mapsto\tt{Cost\:price = \dfrac{100}{\cancel{90}} \times \cancel{9900}}

 \mapsto\tt{Cost\:price = Rs.(100 \times 110)}

 \mapsto\bf{Cost\:price = Rs.11000}

Now,

Total selling price of both washing machine = Rs.9900 + Rs.9900 = Rs.19800 .

Total cost price of both washing machine = Rs.9000 + Rs.11000 = Rs.20000 .

S.P < C.P

→ Loss = Cost price - Selling price

→ Loss = Rs.20000 - Rs.19800

→ Loss = Rs.200

As we know that formula of the loss% ;

 \boxed{\bf{Loss\:\% = \frac{Loss \times 100}{C.P} }}

→ Loss % = 200 × 100/20000

→ Loss % = 20000/20000

Loss % = 1%

Thus,

The whole transaction of loss% will be 1% .

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