If you have ₹800 and you save ₹250 every month, find the amount you have after (i) 6 months (ii) 2 years. Express this as a linear pattern.
Answer: Amount after n months = ₹(800 + 250n). (i) After 6 months: ₹2300. (ii) After 2 years (24 months): ₹6800.
Step-by-step solution
Given: Starting amount ₹800; ₹250 saved every month
Idea: Each month adds the same ₹250, so the amounts form a linear pattern 800 + 250n. Remember to change 2 years into months.
- Linear pattern: 1050, 1300, 1550, … after 1, 2, 3, … months. Amount after n months = ₹(800 + 250n).1 mark
- (i) n = 6: 800 + 250 × 6 = 800 + 1500 = ₹2300.1 mark
- (ii) 2 years = 24 months: 800 + 250 × 24 = 800 + 6000 = ₹6800.1 mark
₹2300 after 6 months and ₹6800 after 2 years; the linear pattern is ₹(800 + 250n) after n months.
Check: Between 6 and 24 months, 18 more months add 18 × 250 = ₹4500, and 2300 + 4500 = 6800 ✓.
Answer to write in the exam
Amount after n months = ₹(800 + 250n)
(i) n = 6: 800 + 250(6) = 800 + 1500 = ₹2300
(ii) 2 years = 24 months: 800 + 250(24) = 800 + 6000 = ₹6800
∴ ₹2300 after 6 months, ₹6800 after 2 years; pattern 800 + 250n
Common mistakes that cost marks
- Using n = 2 for 2 years. The saving is monthly, so n = 24.
- Writing the pattern as 1050n (adding the starting amount every month).
- Forgetting the starting ₹800 and giving 250 × 6 = ₹1500.
How this can come in the exam
MCQ (1 mark)
Meera has ₹1500 and saves ₹400 a month. After 1½ years she has
- ₹2100
- ₹7200
- ₹8700
- ₹9100
Show answer
(C) ₹8700
1½ years = 18 months: 1500 + 400 × 18 = 1500 + 7200 = ₹8700.
Short answer (2 marks)
Raj has ₹600 and saves ₹350 a month. After how many months will he have ₹4800?
Show answer
600 + 350n = 4800 (1 mark) ⇒ 350n = 4200 ⇒ n = 12 months (1 mark).Try one yourself
You have ₹500 and save ₹125 a month. How much will you have after 3 years?
Show answer
500 + 125 × 36 = 500 + 4500 = ₹5000.
More questions like this
- The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. Find both the numbers.
- Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates of the points where these lines cut the y-axis.
- If the temperature of a liquid can be measured in Kelvin units as x K and in Fahrenheit units as y °F, the relation between the two systems of measurement of temperature is given by the linear equation y = 95(x − 273) + 32.
- The work done by a body on the application of a constant force is the product of the constant force and the distance travelled by the body in the direction of the force. Express this in the form of a linear equation in two variables (work w and distance d), and draw its graph by taking the constant force as 3 units. What is the work done when the distance travelled is 2 units? Verify it by plotting it on the graph.
- The graph of a linear polynomial p(x) passes through the points (1, 5) and (3, 11).