Question

1. A dealer allows a discount of 16% to his customers and still gains 5%. Find the marked price of the table which costs him Rs.1200. 2. A shopkeeper allows 25% discount on the marked price of the sarees and still makes a profit of 20%. If he gains Rs.225 over the sale of one saree, find the marked price of the saree. 3. By selling 42 oranges a person loses a sum equal to the selling price of 8 oranges. Find the loss per cent. 4. The marked price of a T.V is re 32500. After allowing a 20% Diwali discount to the customer, a shopkeeper still makes a profit of 30%. Find the cost price of the T.V. 5. A mobile phone is sold for re 3120 at a lose of 4%. What will be the gain or loss percent, if it is sold for rs.3640? Need well explained answer, spam answers will be deleted

Answer 1

Question 1.

A dealer allows a discount of 16% to his customers and still gains 5%. Find the marked price of the table which costs him Rs.1200.

SOLUTION:

Cost Price(C.P) of the table = Rs 1200 (given)

Profit % = 5% (given)

Now,

We can find the profit by the formula

$\boxed{\bf Profit= \frac{Profit \% \times C.P }{100}}$

So,

$\bf Profit = \frac{5 \times 12\not0\not0}{1\not0\not0}$

Profit = Rs 60

And now, we can get the value of the Selling Price

Selling Price(S.P) = Cost price(C.P) + Profit

                            = 1200 + 60

                            = Rs 1260

Also,

Discount % = 16% (given)

The formula to find Marked Price

$\boxed{\bf Marked\ Price(M.P) = \frac{S.P \times 100}{100-Discount \%}}$

$\bf M.P = \frac{1260 \times 100}{100-16}$

$\bf M.P = \frac{126000}{84}$

M.P = Rs 1500

Hence,

The Marked price (M.P) of a table is Rs 1500.

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Question 2.

A shopkeeper allows a 25% discount on the marked price of the sarees and still makes a profit of 20%. If he gains Rs.225 over the sale of one saree, find the marked price of the saree.

SOLUTION:

Let us assume the Marked Price(M.P) of one saree be Rs 100

Given => Discount% = 25%

We can find the Discount by the formula,

$\boxed{\bf Discount=\frac{Discount\%}{100}\times M.P}$

$\bf Discount = \frac{25}{1\not0\not0} \times 1\not0\not0$

So, Discount = Rs 25

Therefore,

The Selling Price of one saree will be

= Marked Price(M.P) - Discount

= 100 - 25

= Rs 75

Also given, Profit% = 20%

So,

$\boxed{\bf Cost Price(C.P)= \frac{S.P\times 100}{100+Profit\%}}$

Cost Price(C.P) of one saree = $\bf \frac{75\times 100}{100+20}$

= $\frac{7500}{120} = \bf Rs\ 62.50$

And,

Gain = S.P - C.P

        = 75 - 62.50

        = Rs 12.50

$Now,$

If the gain is Rs 12.50, then Marked price(M.P) = Rs 100

And,

If the gain is Rs 1 so the Marked Price(M.P) = $\bf \frac{100}{12.50}$

Also given that,

If he gains Rs 225, then the Marked Price(M.P)

= $\bf \frac{100}{12.50} \times 225$

= Rs 1800

Hence,

The Marked Price of a saree is Rs 1800.

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Question 3

By selling 42 oranges a person loses a sum equal to the selling price of 8 oranges. Find the loss percent.

SOLUTION:

let us assume the Seeling Price of one orange be Rs 1

Then

The Selling Price(S.P) of 42 oranges = Rs 1 × 42 = Rs 42

Given - Loss on 8 oranges

= Rs 1 × 8 = Rs 8

Hence,

Cost Price(C.P) of 42 oranges = S.P + Loss

=  Rs 42 + Rs 8

= Rs 50

Now,

The formula for finding the loss%

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

$\bf Loss \% =\frac{8}{5\not0}\times 10\not0$

Loss % = 16%

Hence,

The loss % is 16%

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Question 4.

The marked price of a T.V is rs 32500. After allowing a 20% Diwali discount to the customer, a shopkeeper still makes a profit of 30%. Find the cost price of the T.V.

SOLUTION:

Given:

The Marked Price(M.P) of the T.V = Rs 32500

Discount% = 20%

So,

Discount = $\bf \frac{20\times 32500}{100}$ = Rs 6500

So,

S.P of the T.V = M.P - Discount

S.P = 32500 - 6500 = Rs 26000

Given,

Profit % = 30%

So,

$\boxed{\bf C.P = \frac{100\times S.P}{100+Profit\%}}$

$\bf C.P = \frac{100 \times 26000}{100+30} = \boxed{\bf Rs\ 20000}$

Hence,

The Cost Price(C.P) of the T.V is Rs 20000.

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Question 5

A mobile phone is sold for re 3120 at a loss of 4%. What will be the gain or loss percent, if it is sold for rs.3640?

SOLUTION:

Given,

Selling Price(S.P) = Rs 3120

Loss% = 4%

$\boxed{\bf C.P = \frac{100\times S.P}{100-Loss\%}}$

$\bf C.P = \frac{100\times 3120}{100-4}$

$\bf C.P = \frac{312000}{96} = Rs\ 3250$

Now,

New S.P = 3640

And,

Gain = S.P - C.P

Gain = 3640 - 3250

Gain = Rs 390

Hence,

Gain % = $\bf \frac{Gain}{C.P}\times 100$

Gain % = $\bf \frac{390}{3250}\times 100$

Gain % = 12%

Hence,

The gain % is 12%

Answer 2

$\huge \pink \star \mathfrak{answer} \pink \star$

Q.1↷

Given:-

• Cost price (CP) of the table = Rs.12000
• Profit% = 5%

Now,

We can find the profit by the formula.

$\implies \boxed{profit = \frac{profit\%\times cp}{100} }$

so,

$\implies \boxed{profit = \frac{5 \times 1200}{100} }$

$\implies \boxed{profit = \frac{5 \times 12}{1} }$

$\implies \sf profit = rs.60$

And now, we can get the value of the selling price.

Selling price(SP) = Cost Price(CP) + Profit

= 1200+60

= 1260

Also,

Discount % = 16% (given)

Formula to find Market Price

$\sf{market \: price(m.p) = \frac{sp \times 100}{100 - discount } }$

$\sf{m.p = \frac{1260 \times 100}{100 - 16} }$

$\sf{m.p = \frac{126000}{84} }$

$\sf{m.p = rs.1500}$

Hence,

The Market Price (M.P) of the table is Rs.1500

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Q.2↷

Let us assume the Market Price (M.P) of one saree be Rs.100

Given:-

Discount% = 25%

We can find the discount by this formula

$\sf{discount = \frac{discount\%}{100} \times m.p }$

$\sf{discount = \frac{25}{100} \times 100}$

$\sf{discount = \frac{25}{1} \times 1}$

So, Discount = Rs.25

Therefore

The selling price of one saree will be

• Market price - Discount
• 100 - 25
• 75

Also given, profit% = 20%

$\sf{c.p = \frac{sp \times 100}{100 +profit\% } }$

Cost Price of one saree

$\sf{cp = \frac{75 \times 100}{100 + 20} }$

$= \frac{7500}{120} = \bold{rs.62.50}$

And gain = Sp - Cp

= 75 - 62.50

= Rs.12.50

Now,

if the gain is Rs.12.50, Then Market price = Rs.100

And,

If the gain is Rs.1 so, The Market Price

$\sf{ \frac{100}{25.50} }$

Also given that

If the gains Rs.225 , Then the Market price

$\sf{ \frac{100}{12.50} \times 225 }$

Rs.1800

Hence,

The Market price of the saree is Rs.1800

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Q.3↷

Let us assume the selling price of one orange be Rs.1

Then, the selling price of 42 oranges =

= Rs.1 × 42 = Rs.42

Given:-

Loss on 8 oranges

= Rs.1 × 8 = Rs.8

Hence,

Cost price of 42 oranges = S.P + Loss

= Rs.42 + Rs.8

= Rs.50

Now,

The formula for finding the loss%

$\sf{loss\% = \frac{loss}{c.p} \times 100 }$

$\sf{loss\% = \frac{8}{50} \times 100}$

Loss% = 16%

Hence, The loss% is 16%

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Q.4↷

Given:-

The market price of the T.V = Rs.32500

Discount% = 16%

so,

$\sf{ discount = \frac{20 \times 32500}{100} = rs.6500}$

So,

S.P of the T.V = M.P - Discount

Sp = 32500 - 6500 = Rs.26000

Given:-

Profit% = 30%

so,

$\sf{c.p = \frac{100 \times sp}{100 + profit\%} }$

$\sf{c.p = \frac{100 \times 26000}{100 + 30} = rs 20000}$

Hence, The cp of the T.V is Rs.20000

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Q.5↷

Given:-

• sp = Rs.3120
• Loss% = 4%

$\sf{c.p = \frac{100 \times s.p}{100 - loss\%} }$

$\sf{c.p = \frac{100 \times 3120}{100 - 4} }$

$\sf{c.p = \frac{312000}{96} = rs.3250}$

Now,

New sp = 3640

And,

Gain = S.P - C.P

Gain= 3640 - 3250

Gain = Rs.390

Hence,

Gain% = Gain/C.P×100

Gain% = 390/3250×100

Gain% = 12%

Hence,

The gain% = 12%

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