Bela has ₹100 for pocket money. She spends ₹5 every day. After how many days will she be left with ₹40?
Answer: Amount left after n days = ₹(100 − 5n). 100 − 5n = 40 gives n = 12: she has ₹40 left after 12 days.
Step-by-step solution
Given: Starting amount ₹100; Spends ₹5 each day
To find: The number of days after which ₹40 is left
To find: The number of days after which ₹40 is left
Idea: Each day the amount drops by the same ₹5, so after n days she has spent 5n rupees. This is a linear pattern.
- Make a table:½ mark
Day number 0 1 2 3 4 Amount left (₹) 100 100 − 1 × 5 = 95 100 − 2 × 5 = 90 100 − 3 × 5 = 85 100 − 4 × 5 = 80 - The amount left on the nth day is ₹(100 − 5n).½ mark
- 100 − 5n = 40 ⇒ 5n = 60 ⇒ n = 12.½ mark
- So on the 12th day the amount left will be ₹(100 − 12 × 5) = ₹40. She is left with ₹40 after 12 days.½ mark
After 12 days, Bela will be left with ₹40.
Check: 100 − 12 × 5 = 100 − 60 = 40 ✓.
Answer to write in the exam
Amount left after n days = ₹(100 − 5n)
100 − 5n = 40
5n = 60 ⇒ n = 12
∴ She will be left with ₹40 after 12 days
Common mistakes that cost marks
- Dividing 40 by 5 to get 8 days. ₹40 is what is left; she has spent 100 − 40 = ₹60.
- Writing the amount as 100 + 5n. She spends money, so the amount goes down: 100 − 5n.
- Writing 5 − 100n, mixing up the starting amount and the daily change.
How this can come in the exam
MCQ (1 mark)
A water tank has 900 litres and 45 litres are used every day. The amount left after d days is
- 900 − 45d
- 900d − 45
- 45 − 900d
- 900 + 45d
Show answer
(A) 900 − 45d
45 litres go each day, so after d days 45d litres are used.
Short answer (2 marks)
A phone battery is at 96% and drops by 4% every hour of use. After how many hours will it be at 20%?
Show answer
96 − 4h = 20 (1 mark) ⇒ 4h = 76 ⇒ h = 19 hours (1 mark).Try one yourself
Arjun has ₹250 and spends ₹15 a day. After how many days will he have ₹55 left?
Show answer
250 − 15n = 55 ⇒ 15n = 195 ⇒ n = 13 days.
More questions like this
- 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? - 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.