To find Sale Price Rate per Kg when C.P, Quantity and Profit Rate are given (WP-9: Profit)

MCQs: A shopkeeper purchased 30 kg of sugar for Rs 105. For earning a profit of 10% he should sell the sugar at the rate of;

(a) Rs 3.75 kg (b) Rs 3.85 kg 

(c) Rs 3.90 kg (d) Rs 3.80 kg

Given:

Quantity of Sugar = 30 Kg
Cost price (C.P) = Rs.105
Profit % = 10%

To Find:

Sale price (S.P) per Kg = ?

Solution:

1st Method 

 By using the Formula for Profit % involving Gain is

.....Eqn(1)

And Formula for Gain is

Gain (Profit) = Sale price (S.P) - Cost price (C.P) ....Eqn(2)

From Eqn (1) and (2) we can derive a formula for Cost price (C.P) that is

Sale price (S.P) = (100 % + Profit %) x Cost price (C.P)

So by putting values we get

Sale price (S.P) = (100%+10%) x Rs.105

Sale price (S.P) = (110%) x Rs. 105

Sale price (S.P) = `{\frac{110\times Rs.105}{100}}`

Sale price (S.P) = Rs. 115.5

Sale price (S.P) Per Kg = `\frac{Rs. 115.5}{30}`

Sale price (S.P) Per Kg = Rs. 3.85 Per Kg

2nd Method 

 By using the Formula for Profit % involving Profit is

Or

So by putting values we get

Sale price (S.P) = `{\frac{10\times Rs. 105}{100}}`

Sale price (S.P) = Rs.10.5

Now We know that; 

Sale price (S.P) of 30 kg sugar = cost price + profit 

Sale price (S.P) of 30 kg sugar = Rs.105 + Rs. 10.5

Sale price (S.P) of 30 kg sugar = Rs.11.5

by unitary method

Sale price (S.P) Per kg = `\frac{Rs. 115.5}{30 kg}`

Sale price (S.P) Per kg = 3.85 Per Kg

So, the correct answer is option (b)

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