Question

A man sold a TV for 17000 and lost 15% of its cost. For how much should he sell it to gain 15% ?​

Answer 1

• He sell TV in 23000 to gain 15%.

Step-by-step explanation:

Selling price of TV is 17000

Lost percent is 15%.

• We need Cost price of TV.

Loss = Cost price - Selling price

= C.P - 17000 [Here, C.P is cost price]

$\bold{ Loss \: percent = \cfrac{Loss}{C.P} \times 100}$

Put, loss and loss percent in formula :

$\longrightarrow$ 15 = C.P - 17000/C.P × 100

$\longrightarrow$ 15 × C.P = (C.P - 17000) × 100

$\longrightarrow$ 15/100 × C.P = C.P - 17000

$\longrightarrow$ 3/20 × C.P = C.P - 17000

$\longrightarrow$ 3 C.P = 20×(C.P - 17000)

$\longrightarrow$ 3 C.P = 20 C.P - 340000

$\longrightarrow$ 340000 + 3 C.P = 20 C.P

$\longrightarrow$ 340000 = 20 C.P - 3 C.P

$\longrightarrow$ 340000 = 17 C.P

$\longrightarrow$ 340000/17 = C.P

$\longrightarrow$ 20000 = C.P

Or, $\longrightarrow$ C.P = 20000

Cost price of TV is 20000.

• Now, We will find Selling price of TV. If he is gaining 15%.

Gain percent is 15%.

Gain = Selling price - Cost price

= S.P - 20000 [Here, S.P is Selling price]

Gain is S.P - 20000

$\bold{Gain \: percent = \cfrac{Gain}{C.P} \times 100}$

$\longrightarrow$ S.P - 20000/20000 × 100 = 15

$\longrightarrow$ (S.P - 20000) × 100 = 15 × 20000

$\longrightarrow$ (S.P - 20000)×100 = 300000

$\longrightarrow$ S.P - 20000 = 300000/100

$\longrightarrow$ S.P - 20000 = 3000

$\longrightarrow$ S.P = 3000 + 20000

$\longrightarrow$ S.P = 23000

Therefore,

He sell TV in 23000 to gain 15%.

Answer 2

$\huge{\boxed{\rm{Question}}}$

A man sold a TV for Rupees 17000 and it's lost percentage is 15 of its cost . For how much should he sell it to gain 15% ?

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• A man sold a television for 17000 rupees.

• And he sold it on a loss of 15 percentage of its actual cost.

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• How much should he sell it to gain or profit of 15% ?

$\large{\boxed{\boxed{\sf{Solution}}}}$

• At 23000 Rupees should he sell it to gain or profit of 15%

$\large{\boxed{\boxed{\sf{We \: also \: write \: it \: as}}}}$

• Cost price as C.P

• Selling price as S.P

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: firstly}}}}$

• The question says that a man sold his television for rupees 17000 and he sold this at a loss of 15% means it's loss percentage is 15% . Now it's say that for how much should he sell it to gain 15% ?

$\large{\boxed{\boxed{\sf{How \: to \: do \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Procedure \: of \: the \: question \: is \: given \: below}}}}$

• Firstly we have to know that what are the formulas to find Loss and loss percentage. And we know what is the formula to find both of them. Now we have to put the values according to the both formulas. After putting the values we get 20000 Rupees at the last and it's the C.P / cost price. Now we have to know that what are the formulas to find gain and gain percentage. And we know what is the formula to find both of them. Now we have to put the values according to the both formulas. After putting the values we get 23000 Rupees at the last and it's our final result. Hence, solved :)

$\large{\boxed{\boxed{\sf{Let's \: solved \: it \: properly}}}}$

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

✧ As we know that , what the question says , so according to the question let's carry on ✧

S.P of the telivision = Rupees 17000.

Loss percentage = 15 %

We have to find C.P

♩ Finding cost price ♩

✧ We know that what is the formula of to find the loss ; it's given below ✧

$\small\pink{\texttt{Loss = Cost price - Selling price}}$

↝ Loss = C.P - 17000

Now we have to find loss percentage

✧ We know that what is the formula to find Loss percentage ✧

$\small\pink{\texttt{Loss/CP × 100}}$

$\bold{\blue{\fbox{\blue{Putting the values we get from both formula}}}}$

Loss = C.P - S.P / C.P × 100

↝ 15 = C.P - 17000/C.P × 100

↝ 15 × C.P = (C.P - 17000) × 100

↝ 15/100 × C.P = C.P - 17000

↝ 3/20 × C.P = C.P - 17000

↝ 3 × C.P = 20 × (C.P × 17000)

↝ 3 × C.P = 20 CP × 340000

↝ 340000 + 3 C.P = 20 C.P

↝ 340000 = 20 C.P - 3 C.P

↝ 340000 = 17 C.P

↝ C.P = 340000 / 17

↝ C.P = 20000

Hence, the CP is Rupees 20000

♩ Finding S.P of the television. If the gaining percentage is 15 percentage ♩

✧ We know that what is the formula of to find the gain ; it's given below ✧

$\small\pink{\texttt{Profit = Selling price - cost price}}$

↝ Gain = S.P - 20000

✧ We know that what is the formula to find Loss percentage ✧

$\small\pink{\texttt{Gain/CP × 100}}$

$\bold{\blue{\fbox{\blue{Putting the values we get from both formula}}}}$

↝ S.P - 20000/20000 × 100/15

↝ ( S.P - 20000 ) × 100 = 15 × 20000

↝ ( S.P - 20000 ) × 100 = 300000

↝ S.P - 20000 = 300000 / 100

↝ S.P - 20000 = 3000

↝ S.P = 3000 + 20000

↝ S.P = 23000

Hence, the SP is Rupees 23000

Therefore, At 23000 Rupees should he sell it to gain or profit of 15%

Hope it's helpful

Thank you :)