Profit And Loss - Study Mode

[#31] To gain 10% on selling the mixture of milk and water at the cost price of pure milk, the quantity of water to be mixed with 50 kg of pure milk is = ?
Correct Answer

(B) 5 kg

Explanation

Solution: Let cost price of 1 kg = Rs. 1 Cost price of 50 kg = Rs. 50 $$eqalign{
& Rightarrow { ext{Profit}} = frac{{10}}{{100}} imes { ext{50}} cr
& ,,,,,,,,,,,,,,,,,,,,,,, = { ext{Rs}}{ ext{. 5}} cr
& herefore { ext{Quantity to added}} cr
& = frac{5}{1} = { ext{5 kg}} cr} $$

[#32] A milkman bought 70 litres of milk for Rs. 630 and added 5 litres of water. If sells it at Rs. 9.00 per litres, his profit percentage is = ?
Correct Answer

(D) $$7frac{1}{7}$$%

Explanation

Solution: According to the question, Cost price of 70 litres of milk = Rs. 630 Added 5 litres of water Now, the solution becomes = 75 litres Cost price of water = Rs. 0 ∴ Selling price of 1 litre milk = Rs. 9 Selling price of 75 litres milk = 9 × 75 = Rs. 675 Profit = Selling price - Cost price = 675 - 630 = 45 $$eqalign{
& { ext{Profit}} = frac{{operatorname{Profit} }}{{{ ext{Cost price}}}} imes 100 cr
& = frac{{45}}{{630}} imes 100 cr
& = frac{{50}}{7} cr
& = 7frac{1}{7}\% cr} $$

[#33] A farmer sold a cow and an ox for Rs. 800 and got a profit of 20% on the cow and 25% on the ox. If he sells the cow and the ox for Rs. 820 he gets a profit of 25% on the cow and 20% on the ox. The individual cost price of the cow and the ox is :
Correct Answer

(A) Rs. 530.60, Rs. 130.60 (approx)

Explanation

Solution: Let the C.P. of the cow be Rs. x and that of the ox be Rs. y Then, = 120% of x + 125% of y = 800 $$ Rightarrow frac{{6x}}{5} + frac{{5y}}{4} = 800$$ ⇒ 24x + 25y = 16000 .......(i) And 125% of x + 120% of y = 820 $$ Rightarrow frac{{5x}}{4} + frac{{6y}}{5} = 820$$ ⇒ 25x + 24y = 16400 ......(ii) Adding (i) and (ii), we get : 49x + 49y = 32400 $$ Rightarrow x + y = frac{{32400}}{{49}}......(iii)$$ Substracting (i) from (ii), we get : x - y = 400 ........(iv) Adding (iii) and (iv), we get : $$eqalign{
& 2x = frac{{32400}}{{49}} + 400 cr
& ,,,,,,,,, = frac{{52000}}{{49}} cr
& Rightarrow x = frac{{26000}}{{49}} approx 530.60 cr
& { ext{Putting }}x = frac{{26000}}{{49}}{ ext{ in }}(iii), cr
& { ext{we get}}: cr
& y = frac{{32400}}{{49}} - frac{{26000}}{{49}} cr
& ,,,,,, = frac{{6400}}{{49}} approx 130.60 cr} $$

[#34] The C.P. of two watches taken together is Rs. 840. If by selling one at a profit of 16% and the other at a loss of 12% , there is no loss or gain in the whole transaction, then the C.P. of the two watches are respectively.
Correct Answer

(A) Rs. 360, Rs. 480

Explanation

Solution: C.P. = Cost Price. Let the C.P. of the watches be Rs. x and Rs. (840 - x) ∴ (116% of x) + [88% of (840 - x)] = 840 ⇒ 116x + 73920 - 88x = 84000 ⇒ 28x = 10080 ⇒ x = 360 ∴ Their cost prices are Rs. 360 and Rs. 480

[#35] A space research company wants to sell its two products A and B. If the product A is sold at 20% loss and the product B at 30% gain, the company will not lose anything. If the product A is sold at 15% loss and the product B at 15% gain, the company will lose Rs. 6 million in the deal. What is the cost of product B ?
Correct Answer

(A) Rs. 80 million

Explanation

Solution: Let the cost of product A be Rs. x and B be Rs. y According to first sell 0.80x + 1.3y = x + y ⇒ 0.2x = 0.3y ⇒ x = $$frac{3 ext{y}}{2}$$ . . . . . . (i) According to second sell 0.85x + 1.15y = (x + y) - 6 ⇒ 0.15y = 0.15x - 6 (Multiply by 100) ⇒ 15y = 15x - 600 (Putting the value of x) ⇒ 15y = 15 × $$frac{3 ext{y}}{2}$$ - 600 ⇒ 15y = $$frac{45 ext{y}}{2}$$ - 600 (Multiply by 2 both side) ⇒ 30y = 45y - 1200 ⇒ 15y = 1200 ⇒ y = 80 million