mcqs Math Profit And Loss Mollie purchased 150 kg of wheat at $1350. Due to some unavoidable circumstances, he had to sell the wheat at $7.20 per kg. Calculate his total loss and loss percent in this sale. 150

Question: Mollie purchased 150 kg of wheat at $1350. Due to some unavoidable circumstances, he had to sell the wheat at $7.20 per kg. Calculate his total loss and loss percent in this sale.

(A)  Loss = $1350 and Loss% = 35%
(B)  Loss = $7.20 and Loss% = 25%
(C)  Loss = $270 and Loss% = 20%
(D)  Loss = $270 and Loss% = 30%

Correct Answer Loss = $270 and Loss% = 20%

Solution And Explanation

Solution

Given, Cost price (CP) of 150 kg wheat = $1350

Sale price (SP) = $7.20 per kg

Therefore, loss and loss % = ?

Calculation of cost price of wheat per kg

∵ Cost Price of 150 kg wheat = $1350

∴ Cost Price of 1 kg wheat = ¹³⁵⁰/₁₅₀ = $9

Thus, cost price of wheat per kg = $9

Calculation of loss, when cost price and sale price is known

Here cost price per kg = $9

And, sale price per kg = $7.20

Loss = Cost Price – Sale Price

∴ Loss = $9 – $7.20

⇒ Loss = $1.80

Since, loss in 1 kg = $1.8

Therefore, loss in 150 kg

= 1.8 × 150 = $270

Calculation of loss percent using formula, when loss and cost price is known

Loss% = ^{Loss × 100}/_{Cost price}

Here, Loss per kg = $1.8

And, Cost Price per kg = $9

∴ Loss% = ^{1.80 × 100}/₉

= ^{180 × 100}/_{100 × 9}

= ^{180 20 × 100}/_{100 × 9} = 20%

⇒ Loss = 20%

Therefore, Loss = $270 and Loss% = 20% Answer

Calculation of Loss% using Unitary Method, when loss and cost price is known

Here, Loss per kg = $1.80

And, Cost Price per kg = $9

∵ In $9, loss = $1.80

∴ In $1, loss = ^1.80/₉

∴ In $100, loss = ^1.80/₉ × 100

∴ In $100, loss = ^{1.80 0.2}/₉ × 100

= 0.2 × 100 = 20%

⇒ Loss = 20%

Therefore, Loss = $270 and Loss% = 20% Answer

Calculation of loss% after calculating total sale price

If we calculate the total sale price of rice, then also, the loss percent will be same.

Given, sale price of wheat per kg = $7.20

Total rice = 150 kg

Therefore, sale price of 120 kg wheat = sale price of 1 kg × 150 kg

= $7.20 × 150 = $1080

And, given cost price of 150 kg rice = $1350

Now, Loss = Cost price – Sale price

⇒ Loss = $1350 – $1080 = $270

Now, Loss % = ^{Loss × 100}/_{Cost price}

= ^{270 × 100}/₁₃₅₀

= ^{270 × 100 20}/_{1350 5} = 20%

Therefore, Loss = $270 and Loss% = 20% Answer

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