Question

A trader purchased 80 kg rice at 15 per kg. He also purchased 120kg for rice at 20rs per kg. He mixed both the qualities of rice. What should be his SP per kg so that he may gain 25% in the entire deal
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Answer 1

Working out:

In the question, a shopkeeper buys certain amount of rice at different price depending upon the amount.

Now we need to find the total cost price and then finally we will find the selling price wrt to gain percentage.

So, let's find CP:

Amt. of sugar bought at Rs. 15/kg = 80 kg

CP of this set of sugar = 80 × 15 = Rs. 1200

Amt. of sugar bought at Rs. 20/kg =120 kg

CP of this set of sugar= 120 × 20= Rs. 2400

Then,

Total CP = Rs.1200 + Rs.2400 = Rs. 3600

Total weight of sugar = 80 + 120= 200 kg

Now, Gain % = 25%

Selling price = Cost price + 25% of CP

$\sf{ \longrightarrow{sp = 3600 + \dfrac{25}{100} \times 3600}}$

$\sf{ \longrightarrow{SP = 3600 \bigg(1 + \dfrac{25}{100} \bigg)}}$

$\sf{ \longrightarrow{SP = 3600 \times \dfrac{125}{100} }}$

$\sf{ \longrightarrow{SP = 36 \times 125}}$

$\sf{ \longrightarrow{SP = 4500}}$

This is the total selling price.

Selling price per kg = Rs. 4500 / 200 = Rs. 22.5

So, the final answer is:

$\boxed{ \sf{ \red{ Rs. 22.5}}}$

And we are done !!

Answer 2

★ QUESTION :

A trader purchased 80kg rice at 15 per kg. He also purchased 120 kg for rice at 20₹ per kg. He mixed both the qualities of a rice. What should be its selling price per kg. So, that he may gain 25% in the entire deal.

GIVEN :

• 80kg rice purchased by a trader at an amount = ₹15 per kg.

• 120kg rice purchased by a trader at an amount = ₹20 per kg.

TO FIND :

• The selling price of a trader per kg = ? (at an gain = 25% from entire deal.)

STEP -BY-STEP EXPLAINATION :

➠ 80kg rice purchased by a trader at an amount = ₹15 per kg

Now, we will have to find cost price of the rice as per the given value 80 kg = ₹15 per kg.

⟹ Cost price of the rice at 80kg = 80 × 15 = ₹1,200 (For the first value given)

━━━━━━━━━━━━━━━━━━━━━━━━━━━

➠ 120kg rice purchased by a trader at an amount = ₹20 per kg.

Now, we will have to find the cost price of the rise as per the given value 120kg = ₹20 per kg.

⟹ Cost price of the rice at 120kg = 120 × 20 = ₹2,400 (For the second value given)

━━━━━━━━━━━━━━━━━━━━━━━━━━━

Therefore, the cost price (including the first and second value)

⟹ Cost price = Fist value + Second value

Substituting the values as per the given formula

⟹ Cost price = ₹ 1,200 + ₹2,400

⟹ Cost price = ₹3,600

Now, cost price which we have found here = ₹3,600 (including both the values found)

━━━━━━━━━━━━━━━━━━━━━━━━━━━

Hence, the gain percent that is to be applied = 25% (The gain percent must be = 25%)

ㅤㅤ

$⟹ sᴇʟʟɪɴɢ \: ᴘʀɪᴄᴇ = ᴄᴘ \: + \: ᴠᴀʟᴜᴇ \: ᴏғ \: ɢᴀɪɴ \: ᴏғ \: ᴄᴘ$

So, substituting the values as per the given formula :

$⟹ \: sᴇʟʟɪɴɢ \: ᴘʀɪᴄᴇ = 3600 + \frac{25}{100} \times 3600$

$⟹ \: sᴇʟʟɪɴɢ \: ᴘʀɪᴄᴇ = 3600 (1 \times \frac{25}{100} )$

$⟹ \: sᴇʟʟɪɴɢ \: ᴘʀɪᴄᴇ = 3600 \times \frac{125}{100}$

$⟹ \: sᴇʟʟɪɴɢ \: ᴘʀɪᴄᴇ = 36 \times 125$

$⟹ \: sᴇʟʟɪɴɢ \: ᴘʀɪᴄᴇ = ₹4500$

Now, we will find actual selling price, as per the given :

$⟹ \: sᴇʟʟɪɴɢ \: ᴘʀɪᴄᴇ = \frac{4500}{200} = ₹22.5$

Therefore, the selling price in entire deal = ₹22.5