Harish started work at an annual salary of ₹5,00,000 and received an increment of ₹20,000 each year. After how many years did his income reach ₹7,00,000?
Step-by-step solution
To find: When the annual salary becomes ₹7,00,000
Idea: The yearly salaries form an AP with a = 5,00,000 and d = 20,000. Find which term is 7,00,000; the number of years that have passed is one less than that term number.
- Salaries: 5,00,000, 5,20,000, 5,40,000, … an AP with a = 500000, d = 20000.½ mark
- 500000 + (n − 1) × 20000 = 700000 ⇒ (n − 1) × 20000 = 200000.1 mark
- n − 1 = 10 ⇒ n = 11. So the 11th year’s salary is ₹7,00,000.1 mark
- He started on ₹5,00,000 and got 10 yearly increments, so his income reached ₹7,00,000 after 10 years.½ mark
Check: 5,00,000 + 10 × 20,000 = 5,00,000 + 2,00,000 = 7,00,000 ✓.
Answer to write in the exam
Salaries: 500000, 520000, 540000, … (AP, a = 500000, d = 20000)
500000 + (n − 1) × 20000 = 700000
(n − 1) × 20000 = 200000 ⇒ n − 1 = 10 ⇒ n = 11
∴ Income reached ₹7,00,000 after 10 years (in the 11th year).
Common mistakes that cost marks
- Answering 11 years without explaining: 11 is the term number (11th year); the time that has passed is 10 years.
- Dividing 7,00,000 by 20,000 = 35 and ignoring the starting salary.
- Mixing up lakh commas: ₹5,00,000 is five lakh (500000), ₹20,000 is twenty thousand.
How this can come in the exam
Meera joins a company at a monthly salary of ₹30,000. Each year her monthly salary rises by ₹1,500.
(i) Write her monthly salary in the first three years. (ii) Write the monthly salary in year n. (iii) In which year will it be ₹45,000? (iv) What is her monthly salary in the 8th year?
Show answer
(i) ₹30,000, ₹31,500, ₹33,000 (1 mark). (ii) 30000 + 1500(n − 1) = 28500 + 1500n (1 mark). (iii) 28500 + 1500n = 45000 ⇒ n = 11: the 11th year (1 mark). (iv) 28500 + 12000 = ₹40,500 (1 mark).Try one yourself
A plant is 15 cm tall when planted and grows 4 cm every week. After how many weeks will it be 63 cm tall?
Show answer
15 + 4w = 63 ⇒ w = 12 weeks.
More questions like this
- A child arranges marbles in rows so that the first row has 1 marble, the second has 2 marbles, the third has 3, and so on up to 25 rows. How many marbles does the child use in all?
- Consider the growing pattern of squares shown in the figure. The first four stages of the pattern are shown. If we count the total number of green squares in the four stages of the pattern, we get the sequence 3, 6, 12, 24. Can you predict the number of squares in Stages 5 and 6 of the pattern? In Stages 10, 11 and 12? In Stage 20? At any stage? How is this different from the growing pattern in the figure?
- Is 1, 2, 4, 8, 16, … a geometric progression? If so, what is the common ratio?
- Is 1, 3, 9, 27, 81, … a geometric progression? If so, what is the common ratio?
- Is 1, −1, 1, −1, 1, … a geometric progression? If so, what is the common ratio?
All Sequences and progressions questions · All maths questions