Question

A shopkeper purchased 60 articles at ₹ 150 each. He sold one-third of them at a loss
of 6%.At what price each must he sell the remaining so as to to gain 10% on the whole deal.​

Answer 1

Answer:-

Given:

Total number of articles = 60

CP of each article = Rs. 150

CP of 60 articles = 150 * 60 = Rs. 9000

1/3 of the articles are sold at Loss of 6%.

1/3 of articles = 1/3 * 60 = 20

⟹ CP of 20 articles = 20 * 150 = Rs. 3000

We know that,

SP = (100 - loss%)/100 * CP

⟹ SP of 20 articles = (100 - 6)/100 * 3000

⟹ SP of 20 articles = 94 * 30

⟹ SP of 20 articles = Rs. 2820

Also given that,

Total gain% = 10%

Gain% = Gain/CP * 100

⟹ 10 = Gain/9000 * 100

⟹ 10 * 9000 * 1/100 = Gain

⟹ Rs. 900 = Gain

We know,

Gain = Total SP - Total CP.

We have:

• Total SP = SP of 20 articles + SP of 40 articles.

• Total CP = CP of 60 articles = 9000.

So,

⟹ 900 = 2820 + SP of 40 articles - 9000

⟹ 900 - 2820 + 9000 = SP of 40 articles

⟹ Rs. 7080 = SP of 40 articles

∴ The remaining articles should be sold for Rs. 7080 to gain 10% on the whole transaction.

Answer 2

Question

A shopkeeper purchased 60 article at rupees 158 he sold one third of them at a loss of 6% at what price must he sell the remaining so as to gain 10% on whole deal .

Answer

Given,

• total number of article = 60
• CP of each article = Rs.150

now CP of 60 articles

• 150 × 60 = Rs.9000

$\frac{1}{3} \: of \: \: articles \: are \: sold \: at \: loss \: 6\%$

$\frac{1}{3} \: of \: articles \: =$

$= \frac{1}{3} \times 60$

$= \frac{1}{ \cancel{3}} \times \cancel{60}$

$= 20$

We know that ,

$\huge \bold{sp = \frac{(100 - loss\%)}{100} \times cp}$

now putting the value we get ,

$= > sp \: of \: 20 \: articles \: = \frac{(100 - 6)}{100} \times 3000$

$= > \: sp \: of \: 20 \: artices \: = 94 \times 30$

$= > \: sp \: of \: 20 \: articles = rs.2820$

now total gain percent = 10%

we know that ,

$\huge \bold{ \: gain\% = \frac{gain}{cp} \times 100}$

now putting the values we get ;

$= > 10 = \frac{gain}{9000} \times 100$

$= > gain = 10 \times 9000 \times \frac{1}{100}$

$\bold{ = > gain = rs.900}$

now ,

gain = total sp - total cp

Then, we have ;

1. Sp = SP of 20 articles + sp of 40
2. cp = 9000

Now,

putting the value we get ;

$= > 900 = 2820 + sp \: of \: 40 \: articles \: - 9000$

$= > 900 - 2820 + 9000 = sp \: of \: 40 \: aticles$

$\bold{ = > sp \: of \: 40 \: articles \: = rs.7080}$

he will sell the remaining articles in rupees 7080 in 10% of gain