Profit & Loss Questions with Answer

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Solving a Profit and Loss Problem (লাভ আৰু ক্ষতিৰ সমস্যা সমাধান)

Q. If the Compound Interest for the second year at 4% per annum is ₹520, find the principal. (প্ৰশ্নঃ ৪% বাৰ্ষিক হাৰত দ্বিতীয় বছৰৰ চক্ৰবৃদ্ধি সুত ₹520 হলে, মূলধন কিমান ?)

Options / বিকল্পসমূহ: A) ₹10,000  B) ₹12,500  C) ₹15,000  D) None of these (ইয়াৰ এটাও নহয়)

Trick

Formula: 2nd Year’s CI = P × 104/100 × 4/100

P × 104 × 4/10000 = 520

P = 520 × 10000/104 × 4

P = 5200000/416 = 12,500

Ans / উত্তৰ: B) ₹12,500

Shortcut Formula

P = 2nd Year’s CI × 10000 / R(100+R)​​

Here, P = 520 × 10000 / 4 × 104 = 12,500

Ans: ₹12,500

Q. A shopkeeper buys a table for ₹2,400 and sells it for ₹2,880. Find the profit or loss and profit or loss percentage. প্ৰশ্ন: এজন দোকানীয়ে এখন টেবুল ₹2,400 টকাত কিনি ₹2,880 টকাত বিক্ৰী কৰিলে। লাভ বা ক্ষতি আৰু লাভ বা ক্ষতিৰ শতকৰা হাৰ নিৰ্ণয় কৰা।

Solⁿ

1at: Find the Profit or Loss (১st: লাভ বা ক্ষতি নিৰ্ণয়) 

Profit = Selling Price − Cost Price (লাভ = বিক্ৰী মূল্য − ক্ৰয় মূল্য)

= ₹2,880 − ₹2,400 = ₹480

Since the Selling Price is greater than the Cost Price, there is a Profit.(বিক্ৰী মূল্য ক্ৰয় মূল্যতকৈ বেছি, সেয়ে লাভ হৈছে।)

2nd: Find the Profit Percentage (লাভৰ শতকৰা হাৰ নিৰ্ণয়)

Profit % = (Profit ÷ Cost Price) × 100 {লাভ % = (লাভ ÷ ক্ৰয় মূল্য) × 100}

= (480 ÷ 2400) × 100 = 20%

Ans: Profit (লাভ) = ₹480

Profit Percentage(লাভৰ শতকৰা হাৰ) = 20%

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1. Calculating Profit

Q: A boy buys a toy for $15 and sells it for $20. Find the profit.

Solⁿ:

Profit = Selling Price − Cost Price
Profit = 20 − 15
Profit = $5

Ans: Profit = $5

2. Calculating Loss

Q: A girl buys a book for $12 and sells it for $8. Find the loss.

Solⁿ:

Loss = Cost Price − Selling Price
Loss = 12 − 8
Loss = $4

Ans: Loss = $4

3. Profit Percentage

Q: Cost Price = $50, Selling Price = $60. Find Profit Percentage.

Solⁿ:

Profit = 60 − 50 = 10

Profit % = (Profit ÷ Cost Price) × 100
= (10 ÷ 50) × 100
= 0.2 × 100
= 20%

Ans: 20% Profit

4. Finding Cost Price

Q: Selling Price = $30, Profit = $5. Find Cost Price.

Solⁿ:

Cost Price = Selling Price − Profit
Cost Price = 30 − 5
Cost Price = $25

Ans: $25

5. Extra Practice (Mixed)

Q: A pen is bought for $10 and sold for $13. Find profit.

Solⁿ:

Profit = 13 − 10 = $3

Ans: $3

Q. A scheme offers "Buy 6, Get 4 Free" on identical items having the same MRP. Find the percentage discount received. (একে MRP-যুক্ত একেধৰণৰ বস্তুত "৬ টা কিনক, ৪ টা বিনামূলীয়াকৈ পাওক" ধৰণৰ অফাৰ দিয়া হৈছে। লাভ কৰা ছাড়ৰ শতাংশ নিৰ্ণয় কৰা।)

Options: A. 67.67% | B. 66.67% | C. 41% | D. 40%

Solⁿ(সমাধান):

Buy 6 items and get 4 items free.

Total items received = 6 + 4 = 10

Discount % = Free Items / Total Items × 100 = 4/10 × 100 $$=\; 40\%$$

Ans / উত্তৰ: D. 40%

HCF and LCM

Q. The HCF of two numbers is 18 and their LCM is 1512. If one of the numbers is 126,find the positive difference between the two numbers

(দুটা সংখ্যাৰ HCF = 18 আৰু LCM = 1512। যদি ইয়াৰ ভিতৰত এটা সংখ্যা 126 হয়, তেন্তে সংখ্যা দুটাৰ মাজৰ ধনাত্মক পাৰ্থক্য নিৰ্ণয় কৰা।)

Options: A. 216 | B. 126 | C. 256 | D. 90

Solⁿ(সমাধান):

Formula: First Number × Second Number = HCF × LCM

126 × x = 18 × 1512

$$26\times x=$$27216 126

x = 27216 / 126 = 216 

Second number = 216

Positive difference: 216 − 126 = 90 

Ans / উত্তৰ: D. 90

Q. If the Compound Interest (CI) for the second year at 10% per annum is ₹660, find the principal. (প্ৰশ্নঃ ১০% বাৰ্ষিক হাৰত দ্বিতীয় বছৰৰ চক্ৰবৃদ্ধি সুত ₹660 হলে, মূলধন কিমান ?)

Options / বিকল্পসমূহ: A) ₹6,000  B) ₹8,000  C) ₹10,000  D) None of these (ইয়াৰ এটাও নহয়)

Trick

Second year's CI = 10% of Amount after 1st year

Amount after 1st year = 660 × 10 = ₹6,600

Principal = 6,600 ÷ 1.10 = ₹6,000

Ans / উত্তৰ: A) ₹6,000

Shortcut Formula : Principal = 2nd Year’s CI × 1000 / Rate × (100 + Rate)​​

For this question: P = 660 × 1000 / 10 × 110 = 660000 / 1100 = 6000

Ans: ₹6,000