Question

By selling two watches for ru. 780 each,Ravi gains 20 percent on one and loses 20 percent on the other. Find his net gain or loss per cent. ​

Answer 1

${\underline{\underline{\sf{Answer}}}}$

Ravi will suffer loss of 4% .

${\underline{\underline{\sf{Given}}}}$

• Ravi sold 2 watches each at Rs 780

• He gain 20% on 1st watch .

• And loss 20% on 2nd watch .

We have to find the net gain or loss percentage .

${\underline{\underline{\sf{Solution}}}}$

In case of 1st watch :-

→ Selling cost = Rs 780 .

→ Profit percentage = 20%

→ Cost price = x

C.P = 100 × SP / 100+gain

Using this formula :-

→ $\sf{\frac{100}{100+20} \times 780}$

→ $\sf{\frac{100}{120} \times 780}$

→ $\sf{10 \times 65 = 650 }$

→ So cost cost price of first watch is 650 rupees .

In case of 2nd watch :-

→ Selling price = Rs 780

→ Loss percentage = 20%

→ Cost price = y

CP = 100 × SP/100-loss

Now using this formula

→ $\sf{\frac{100}{100- 20} \times 780}$

→ $\sf{\frac{100}{80} \times 780}$

→ $\sf{25 \times 39 = 975}$

So thecost price of second watch is 975 rupees.

Combining both cases

→ Cost price = 975 + 650 = 1625

→ Selling price = 780 + 780 = 1560

Cost price is greater than selling price it implies that Ravi occurred a loss .

→ Loss = 1625 - 1560 = Rs 65 .

$\boxed{\sf{Loss \: Percentage = \frac{Loss}{CP} \times 100}}$ %

→ $\sf{\frac{65}{1625} \times 100}$

→ $\sf{\frac{6500}{1625} = 4}$

So the loss occurred by Ravi is 4% .

Short cut Method :-

Note → In this type of questions the owner will definitely occur a loss .

$\boxed{ \sf{loss \: = \: ( { \frac{x}{10} )}^{2}} }$

Here x is the gain and loss percentage .

Using this formula :-

→ $\sf{\frac{20 \times 20}{10 \times 10} }$

→ 2 × 2 = 4

So 4 % loss .

Answer 2

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$\huge\tt{GIVEN:}$

• By selling two watches for ru. 780 each,
• Ravi gains 20 percent on one and loses 20 percent on the other.

____________________________

$\huge\tt{TO~FIND:}$

• Find his net gain or loss per cent.

____________________________

$\huge\tt{SOLUTION:}$

______________________________

FIRST WATCH-

S.P = ₹ 780

profit = 20%

Let the cost price of first watch be x

C.P = 100×SP/100+gain

100/100+20 × 780

100/120 × 780

100/120 × 780

10 × 65

650

Now, The Cost Price of first watch is ₹650

____________________________

SECOND WATCH-

S.P = ₹ 780

Loss = 20%

Let the cost price of first watch be y

C.P = 100×SP/100- Loss

100/100-20 × 780

100/80 × 780

25 × 39

975

Now, The Cost Price of first watch is ₹650

____________________________

BOTH WATCHES-

C.P = ₹ (975+650) = ₹1625

S.P = ₹ (780+780) = ₹1560

LOSS = ₹ (1625-1560) = ₹65

Loss Percent = 65/1625 × 100

Loss Percent = 6500/1625

Loss Percent = 4%

Hence,

Loss Percentage is 4

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