A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the nth month.
Step-by-step solution
To find: The amounts month by month, and an expression for the nth month
Idea: Assume she saves all her pocket money. Each month the balance grows by the same ₹150, so after n months ₹150 × n has been added to ₹500.
- End of month 1: 500 + 150 = ₹650.½ mark
- From the second month onwards, add ₹150 each time:1 mark
Month 1 2 3 4 5 … n Amount (₹) 650 800 950 1100 1250 … 500 + 150n - After n months, 150n rupees have been added, so the amount in the nth month = ₹(500 + 150n).1 mark
- This is a linear expression in n: the amount rises by the same ₹150 every month.½ mark
- Note: if the ₹500 is taken as her balance at the end of the first month (with pocket money added only from the second month), the expression becomes 500 + 150(n − 1) = ₹(150n + 350). State which reading you use.
Check: n = 4: 500 + 600 = 1100, which matches the table ✓.
Answer to write in the exam
Month 1: 500 + 150 = ₹650
Month 2: ₹800; Month 3: ₹950; Month 4: ₹1100; Month 5: ₹1250; …
Amount after n months = 500 + 150 × n
∴ Amount in the nth month = ₹(500 + 150n)
Common mistakes that cost marks
- Writing 650n, which adds the ₹500 again every month. The ₹500 is there only once.
- Writing 500n + 150 (swapping the fixed amount and the monthly amount).
- Giving only the expression without the month-by-month amounts that the question also asks for.
How this can come in the exam
Raj has ₹1200 saved and adds ₹250 every month. The amount after n months is
- ₹1450n
- ₹(1200 + 250n)
- ₹(1200n + 250)
- ₹(250 − 1200n)
Show answer
(B) ₹(1200 + 250n)
₹1200 once, plus ₹250 for each of the n months.
A plant nursery has 80 saplings and plants 35 more every week. Write the number of saplings after w weeks and find it after 12 weeks.
Show answer
80 + 35w (1 mark). After 12 weeks: 80 + 420 = 500 saplings (1 mark).Try one yourself
A piggy bank has ₹300, and ₹75 is added every month. Write the amount after n months and find it after 10 months.
Show answer
₹(300 + 75n); after 10 months ₹1050.
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