A man gets an employment of Rs.1000per month with an annual increment of Rs.50 . What does he earn in 10 years
Answers
Answer:
It's a very simple arithmetic problem.
Let's break it down.
Rupees 1000 per month is his income for his first year and that's his base income. So obviously he earns 12000 (1000*12 months) rupees in his first year.
Not considering the increase, he'll earn 120000 Rupees if he earns money every month for 12 months in 10 years. (1000 * 12months * 10 years).
Now let's deal with the increase. Every year his salary increases by 50 rupees per month. So for the second year he'll be earning 1000+50 that is 1050 rupees per month. In third year it'll be 1050+50 which is 1100 rupees p.m and so on.
Now let's deal with the increase like arithmetic sequence. On his second year he'll be earning 50 RPS p.m (excluding his base salary which we have already calculated in the beginning). So if he earns 50 p.m in year two, he'll earn 50+50 that is 100 p.m in year 3 and so on. In the tenth and final year he'll earn 50*(10–1) that is 450 r.p.s p.m. Then apply the formula.
½.n.(a+l)
So n is the number of years. Remember we're not counting the first year since there was no increase in that particular year. So from year 2 to 10 there are 9 years hence n is 9. a is the first value in the sequence which is 50. And l is the last value which is 50*9(total number of years with increased salary).
Therefore,
½.9(50+450) = 2250
Multiply 2250 by 12 which is the total number of months in a year. You'll get 27000 rupees.
So in 10 years he received, (1000*12*10) + ((½.9.(50+450)*12) = 147000 rupees.
It's a very simple calculation, I just elaborated every step. Hope you understand. Cheers!
his annual income: 1000×12+50=12050
In 10 years
12050×10=120500
so, he will earn Rs.120500 in 10 years