A spice trader takes a loan (debt) of ₹850. The next day, he makes a profit (fortune) of ₹1,200. The following week, he incurs a loss of ₹450. Write this sequence as an equation using integers and calculate his final financial standing.
Step-by-step solution
Idea: Write debts and losses as negative integers and profits as positive integers, then add them in order.
- Loan (debt) of ₹850 → −850. Profit of ₹1,200 → +1200. Loss of ₹450 → −450.½ mark
- Equation: (−850) + 1200 + (−450) = x, where x is his final standing.½ mark
- (−850) + 1200 = 350 (the profit clears the loan and leaves ₹350). Then 350 + (−450) = −100.½ mark
- x = −100: his final standing is a debt of ₹100.½ mark
Check: Total gains 1200, total debts and losses 850 + 450 = 1300; 1200 − 1300 = −100 ✓.
Answer to write in the exam
Loan = −850, profit = +1200, loss = −450
Final standing = (−850) + 1200 + (−450)
= 350 + (−450)
= −100
∴ He has a debt of ₹100.
Common mistakes that cost marks
- Writing the loan as +850, because he ‘receives’ money. A loan is a debt, so it is −850.
- Getting the size right but the sign wrong: answering ‘₹100 profit’.
- Adding all three as positives: 850 + 1200 + 450 = 2500.
How this can come in the exam
A shop owner gains ₹500 on Monday, loses ₹720 on Tuesday and gains ₹150 on Wednesday. His net result is
- ₹70 profit
- ₹70 loss
- ₹1370 profit
- ₹370 loss
Show answer
(B) ₹70 loss
500 − 720 + 150 = −70, a loss of ₹70.
A school canteen starts the month with a debt of ₹1,500 to its supplier. In week 1 it earns ₹2,300, in week 2 it pays ₹900 for repairs, and in week 3 it earns ₹650.
(i) Write the debt and the repairs as integers. (ii) Write one equation for the canteen’s position after week 3. (iii) Find the position. (iv) Is the canteen in debt or in profit?
Show answer
(i) −1500 and −900 (1 mark). (ii) (−1500) + 2300 + (−900) + 650 = x (1 mark). (iii) x = 550 (1 mark). (iv) In profit: it has ₹550 after clearing the debt (1 mark).Try one yourself
Meena owes ₹300, then earns ₹480, then spends ₹260. Write an integer equation for her position and solve it.
Show answer
(−300) + 480 + (−260) = −80: she owes ₹80.
More questions like this
- Calculate the following using Brahmagupta’s laws:
- Explain, using a real-world example of debt, why subtracting a negative number is the same as adding a positive number (e.g., 10 − (−5) = 15).
- As society grew more complex, measuring became just as important as counting. If a farmer divides a field of wheat among his three children, how much does each get? If a recipe calls for half a cup of ghee, how do we represent that mathematically?
- Can you explain why we need q ≠ 0 in the definition of a rational number?
- 1. While adding or subtracting two rational numbers having different denominators, how will you make the denominators equal?
2. Verify the distributive law for rational numbers.