Bela has ₹100 for pocket money. She spends ₹5 every day. Observe that the amount left on the nth day will be ₹(100 − 5n).
What amount will be left on the 15th day? How many days will it take for the entire amount to be spent?
Answer: On the 15th day ₹(100 − 75) = ₹25 is left. The money runs out when 100 − 5n = 0, that is, after 20 days.
Step-by-step solution
Given: Amount left on the nth day = ₹(100 − 5n)
Idea: Put n = 15 into 100 − 5n. “The entire amount is spent” means the amount left is 0, so solve 100 − 5n = 0.
- 15th day: 100 − 5 × 15 = 100 − 75 = ₹25.1 mark
- All spent: 100 − 5n = 0 ⇒ 5n = 100 ⇒ n = 20.½ mark
- It takes 20 days to spend the whole ₹100.½ mark
₹25 will be left on the 15th day, and the whole amount will be spent in 20 days.
Check: 20 days × ₹5 = ₹100 ✓.
Answer to write in the exam
Amount left on nth day = ₹(100 − 5n)
15th day: 100 − 5(15) = 100 − 75 = 25
100 − 5n = 0 ⇒ 5n = 100 ⇒ n = 20
∴ ₹25 is left on the 15th day; the money lasts 20 days
Common mistakes that cost marks
- Giving ₹75 for the 15th day. ₹75 is what she has spent; the question asks what is left.
- Solving 100 − 5n = 0 as n = 100 − 5 = 95.
- Answering 21 days by counting day 0 as a day of spending.
How this can come in the exam
MCQ (1 mark)
A candle is 30 cm long and burns 1.5 cm every hour. It burns out completely after
- 15 hours
- 20 hours
- 28.5 hours
- 45 hours
Show answer
(B) 20 hours
30 − 1.5h = 0 ⇒ h = 20.
Short answer (2 marks)
A bus pass has 60 rides and 2 rides are used every day. How many rides remain after 18 days, and after how many days is the pass used up?
Show answer
60 − 2 × 18 = 24 rides (1 mark). 60 − 2d = 0 ⇒ d = 30 days (1 mark).Try one yourself
A pot of rice has 3 kg and 0.25 kg is used each day. How much is left after 8 days, and when will it run out?
Show answer
3 − 0.25 × 8 = 1 kg left. 3 − 0.25d = 0 ⇒ d = 12 days.
More questions like this
- An auto-rikshaw fare starts at ₹25 and remains the same for the initial 2 km. Then it increases by ₹15 per km. What will be the fare for a travel of 10 km?
- Observe that the total fare for a travel of n km will be ₹25 + 15 × (n − 2) = 15n − 5, when n ≥ 2.
For how many km will the fare be ₹130? - 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.
- A rally starts with 120 members. Each hour, 9 members drop out of the group. How many members will remain after 1, 2, 3, … hours? Find a linear expression to represent the number of members at the end of the nth hour.
- Suppose the length of a rectangle is 13 cm. Find the area if the breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm. Find the linear pattern representing the area of the rectangle.