Question

A shopkeeper sells two qualities of tea at the rates of Rs. 36 per kg, and Rs. 44 per kg, gaining 20% and 10% profit respectively. If he mixes the two variants in the ratio 1:4 and sells the mixture at Rs. 41.8 per kg, what is his gain% or loss%?​

Answer 1

The shopkeeper sells two kinds qualities of wheat at 11 per kg and 24 per kg.

➡️ On the $11, he gains 10% profit.

Let the cost price be x.

So, x + 10/100 * x = 11

Or, x + x/10 = 11

Or, 11x/10 = 11

Or, x = 10.

So, cost price of the first quality of wheat is $10. ⬅️

➡️ On the $24, he gains 20% profit.

Let the cost price be y.

So, y + 20/100 * y =24

Or, y + y/5 = 24

Or, 6y/5 = 24

Or, y = 24 * 5/6 = 20.

So, the Cost price of second quality of the wheat is $20. ⬅️

He mixes them is the ratio 2 : 3.

Now, sum of ratios is = 5.

Thus, 2/5 part is the wheat of first quality and 3/5 part is the wheat of second quality.

Thus, Cost price of the mixture

= $ (2/5 * 10 + 3/5 * 20)

= $ (4 + 12)

= $ 16.

➡️ Again, the shopkeeper sells it at $12.8 per kg.

So, it is obvious that Cost price > Selling price, so there is a loss.

Loss = $ (16 - 12.8)

= $ 3.2

Now, Loss percentage

= 3.2/16 * 100 %

= 1/5 * 100 %

= 20 %

➡️ Hence, there is a loss of 20%

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Answer 2

Answer:

% PROFIT=PROFIT/CP *100 = 3.8/38*100 =10

Step-by-step explanation:

The shopkeeper sells two kinds qualities of tea at 36 per kg and 44 per kg.

(MIX 1 )SP=36

SP = 120/100*CP

36=120/100*CP

Cost price(MIX1)=30

(MIX 2)SP=44

SP = 110/100*CP

44=120/100*CP

Cost price(MIX2)=40

therefore we can calculate actual Cost of mix1,mix2

NEW MIX 1:4,TOTAL PARTS ARE 1+4 =5 PARTS

SO,  1 PART OUT OF 5 IS OF MIX 1 + 4 PART 1 PART OUT OF 5 IS OF MIX 2

       1/5CP MIX1 +4/5CP MIX2

      30/5+ (4*40)/5 =190/5 = 38 IS THE Cost price  OF 1 PART

SO,1 KG OF NEW MIX COSTS RS 38

AND HE SELLS AT RS 41.8

SO HE IS AT PROFIT

PROFIT= SP-CP =41.8 -38 = 3.8

% PROFIT=PROFIT/CP *100 = 3.8/38*100 =10