Question

6. A man sold two washing machines for rs.9900
each. He sold one at a gain of 10% and the other
at a loss of 10%. Find his gain or loss % in the
whole transaction.​

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

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

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

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

• 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% .