Find Profit & Cost 6

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Q. Find the cost price of an article sold for ₹1470 at a profit of 16 2/3%. এক বস্তু ১৬ 2/3% লাভত ₹1470ত বিক্ৰী কৰা হৈছিল, ইয়াৰ ক্ৰয় মূল্য কিমান ?

Soln

1^st : Convert Profit % into Fraction / % → Fraction

• 16 2/3% = 50/3 % = 16.666…%

2^nd : Use Unit Method / একক পদ্ধতি

• Assume CP = 100 units → SP = 100 + Profit%


• SP = 100 + 16 2/3 = 116 2/3 units = 350/3 units


• Ratio → CP : SP = 100 : 116 2/3 = 300 : 350 units

3^rd : Find Value of 1 unit / ১ এককৰ মূল্য

SP = ₹1470 → 350 units = 1470

• 1 unit = 1470 ÷ 350 = ₹4.2

4^th : Find CP / ক্ৰয় মূল্য উলিওৱা

CP = 300 units → 300 × 4.2 = ₹1260

Ans / উত্তৰ: Cost Price = ₹1260, ক্ৰয় মূল্য = ₹1260

Trick 1: Always convert fractional % into improper fraction → easier unit calculation.ভাগ % কেই improper fractionত ৰূপান্তৰ কৰক → একক পদ্ধতিত সৰল গণনা হয়।

Trick 2: Always scale units proportionally → fast CP calculation.ট্ৰিক: একক অনুযায়ী proportion কৰি CP ৰেট সৰলভাৱে উলিওৱা যায়।

Short Trick Formula / ট্ৰিক ফৰ্মুলা

CP = 1470×100 / 1162/3 = 1260

Trick 3: Use the CP = SP × 100 / (100 + Profit%) formula directly for all fractional % → saves time in exams. ট্ৰিক: যিকোনো fraction লাভ % ত এই formula সৰলভাৱে ব্যৱহাৰ কৰিব পাৰি।

Q. A shopkeeper sells an article at 16 2/3% profit on Selling Price (SP). Find the actual profit percentage on the Cost Price (CP). একজন দোকানদাৰে বিক্ৰয় মূল্যত 16 2/3% লাভ দেখাই বস্তুটো বিক্ৰী কৰিলে, সঁচা লাভ শতাংশ কিমান ?

সমাধান

16 2/3% = 16.666…% = 50/3%

SP ভিত্তিত লাভ = 16.666…% = 1/6 (one-sixth)

ধৰি লওঁ:

• SP = 6 অংশ


• Profit = 1 অংশ


• CP = SP - Profit = 6 - 1 = 5 অংশ

Real Profit % = (Profit / CP) × 100

= (1/5) × 100

= 20% লাভ

Soln

16 2/3% = 16.666…% = 1/6

Let:

• SP = 6 units


• Profit = 1 unit


• CP = SP - Profit = 6 − 1 = 5 units

Actual Profit % = (Profit/CP) × 100

= (1/5) × 100

= 20%

Quick Trick / সৰু ট্ৰিক

If profit is given on SP → Convert to CP profit:

=16 2/3/100−16 2/3×100 = 20% Ans / উত্তৰ

20% সঁচা লাভ (Real Profit)

Q. If the Cost Price (CP) and Selling Price (SP) of an article are in the ratio 20 : 17, find the loss percentage.

Options: (a) 15%  (b) 12%  (c) 17%  (d) 21%

Solⁿ

CP : SP = 20 : 17

Loss = 20 − 17 = 3

Loss % = Loss / CP×100 = 3/20×100 = 15%

Ans: (a) 15%

Exam Trick : When CP : SP = a : b and a > b,

 Loss % = a−b/a​×100

Here: (20 - 17)/20 × 100 = 15%

Q. 3 pencils and 5 pens together cost Rs.101, whereas 5 pencils and 3 pens together cost Rs.91. The cost of 2 pencils and 2 pens together is:     

Option : - (a) Rs.45 (b) Rs.36 Ich Rs.48 (d) Rs.32

Solⁿ

Here, P = cost of 1 pencilQ = cost of 1 pen

Given two equations:

Add them: (3P + 5P) + (5Q + 3Q) = 101 + 91                                         

                                           8P + 8Q = 192

                                           2P + 2Q = 48 (Because 8P + 8Q is 4 times bigger than 2P + 2Q, so  divide by 4.)

Ans : 2 pencils + 2 pens cost = Rs.48