Question

Mr. Sinha sold two tape-recorders for 990 each; gaining 10% on one and losing 10% on the other. Find his total loss or gain, as percent, on the whole transaction.​

Answer 1

$\Huge\boxed{\tt\green{✠Answer}}$

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✴️ Loss Percent = 1 % ✴️

Given:

Selling price of two tape recorders is Rs 990 each.

On one recorder he gains 10% and on other he losses 10%.

To Find:

What is his loss of gain percent in whole transaction ?

Solution: In first condition on first recorder

S.P = Rs 990.

Gain % = 10%.

As we know to find C.P when S.P and gain % are given we use the formula

▪️C.P = (100/100 + gain %) × S.P ▪️

$\bf{\longrightarrow C.P = \bigg( \dfrac{100}{100} + 10 \bigg) × 990}$

$\bf{ \longrightarrow \: \dfrac{100}{110} × 990}$

$\bf {\longrightarrow \dfrac{99000}{110} }$

$\boxed{ \bf{\implies 900}}$

So cost price of first recorder is Rs 900.

Now, in second condition on second recorder

S.P = Rs 990

Loss % = 10 %

Using formula

$\bf{♠C.P = \bigg( \dfrac{100}{100} – loss \% \bigg) × S.P}$

$\bf{\longrightarrow C.P = \bigg ( \dfrac{100}{100} – 10 \bigg) × 990}$

$\bf{\longrightarrow \dfrac{100}{90} × 990}$

$\bf{\longrightarrow \dfrac{99000}{90} }$

$\boxed{ \bf{\implies \: 1100}}$

So cost price of second recorder is Rs 1100.

Lets find total s.p & c.p of both recorders.

➜Total S.P = Rs (990 + 990)

➜ 1980

➜Total C.P = Rs (900 + 1100)

➜Rs 2000

On comparing both C.P and S.P

C.P > S.P (Here is loss)

• Loss = C.P – S.P

• Rs (2000 – 1980) = Rs 20

$\bf{★ Loss \% = \bigg ( \dfrac{Loss}{C.P} × 100 \bigg)}$

$\bf{➨ \bigg ( \dfrac{20}{2000} × 100 \bigg)}$

$\bf{➨ \dfrac{2000}{2000} }$

$\huge \boxed{ \tt{ 1 \%}}$

$\bf \purple{Hence \: his \: loss \: percent \: on \: whole \: transaction \: is \: 1 \%.}$

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Answer 2

GIVEN :-

• Mr. Sinha sold two tape-recorders for 990 each.

• Gain 10% on one.

• Loss 10% on the other.

We have to find :-

• His total loss or gain, as percent, on the whole transaction.

Solution :-

First tape recorder :

SP = Rs. 990

Gain% = 10%

Using formula

CP = (100/100 + gain %) × SP

$\rightarrow CP \: = \: (\frac{100}{100 + 10}) \times \: 990 \\ \\ \rightarrow \: \frac{100}{110} \: \times 990 \\ \\ \rightarrow \: 100 \: \times 90 \: = \green{900}$

So cost price of first recorder is Rs 900.

Second tape recorder :

SP = Rs 990

Loss % = 10 %

Using formula

CP = (100/100 - Loss %) × SP

$\rightarrow \: CP = (\frac{100}{100 - 10}) \: \times 990 \\ \\ \rightarrow \: \frac{100}{90} \times \: 990 \\ \\ \rightarrow \frac{99000}{90} = \blue{1100}$

So cost price of second recorder is Rs 1100.

Let us find total SP & CP of both recorders.

➜Total SP = Rs (990 + 990) = Rs 1980

➜Total CP = Rs (900 + 1100) = Rs 2000

On comparing both CP and SP

CP > SP (So here is loss)

Loss = CP – SP

Rs (2000 – 1980) = Rs 20

Loss % = (Loss / CP) × 100

$\rightarrow \: (\frac{20}{2000} \times \: 100) \\ \\ \rightarrow \: \frac{2000}{2000}$

= 1 %

Hence, his loss percent on whole transaction is 1%.

$\boxed{ \star \: Be \: Brainly}$