Question

A shopkeeper sells the rubber bands at 5 for a rupee gaining 40%. How many did he buy for a rupee?

Answer 1

Information provided with us:

➪ Selling price of 5 rubber bands

$\implies \sf \: 1 \: Rs$

➪Gain percent

$\implies \sf \: 40 \: \%$

What we have to calculate :

• ➪ The required number of rubber bands buy for a ruppee

✰ Solution ༄

$\clubsuit \: \rm \: C.P \: of \: 5 \: rubber \: bands :$

$\bigstar \: \: \sf\boxed{\bold{\pink{Rs \bigg(1 \times \dfrac{100}{140}\bigg)}}}\: \: \: \bigstar$

$\bigstar \: \: \sf\boxed{\bold{\red{Rs\bigg( \dfrac{100 \div 20}{140 \div 20}\bigg)}}}\: \: \: \bigstar$

$\bigstar \: \: \sf\boxed{\bold{\orange{Rs\bigg( \dfrac{5}{7}\bigg)}}}\: \: \: \bigstar$

✰Note Here ༄

• ➡ C.P = Cost price

✰Now ༄

$\implies \bf For \: Rs \: \dfrac{5}{7} , rubber \: bands \: bought$

$\implies \sf\bold{\red{5}}$

$\implies \bf For \: Rs \: 1 , rubber \: bands \: bought$

$\implies \sf \bigg(5 \times \dfrac{7}{5}\bigg)$

$\implies \sf \bigg( \dfrac{5 \times 7}{5}\bigg)$

$\implies \sf \bigg( \dfrac{35}{5}\bigg)$

$\implies \sf\bold{\red{7}}$

✰Therefore༄

$\rm \therefore \: The \: required \: number \: of \: rubber \:$

$\rm \: bands \: buy \: for \: a \: ruppee \: is \: \bf{7 . }$

Answer 2

Given :

Profit by selling 5 rubber bands for ₹1 = 40%

To Find :

Number of rubber bands that he bought in ₹1

Solution :

Selling price of 5 rubber bands = ₹1

Selling price of 1 rubber band = $\frac{1}{5}$ = ₹0.2

We know,

  Profit %   = $\frac{Profit}{CP}$ × 100%             (CP = Cost Price)

⇒    40%     =  $\frac{SP - CP}{CP}$ × 100%

⇒    0.4       =  $\frac{0.2 - CP}{CP}$

⇒    0.4CP  =  0.2 - CP

⇒     1.43CP  =  0.2

⇒      CP     =  $\frac{0.2}{1.43}$

∴      CP     = ₹0.143

In ₹0.143, shopkeeper bought 1 rubber band

In ₹1, shopkeeper bought $\frac{1}{0.143}$ rubber bands

                                         = 7 rubber bands

Therefore, the shopkeeper bought 7 rubber bands for a rupee.