Question

The rate of monthly salary of a man increases annually in A.P. He was drawing Rs 40,000 per month during the eleventh year of his swrvice and Rs 76,000 per month during the 29th year of his service. Find his starting salary and the rate of annual increment. What should be his salary at the time of his retirement just on the complition of 36 years of service?​

Answer 1

Hey guys need any help than than comment

Answer 2

Answer:

His starting salary was 20,000 and the rate of annual increment is 10%.

His salary at his time of retirement will be 90,000.

Step-by-step explanation:

Given:- Rs. 40,000 during 11th year of service.

Rs. 76,000 during 29th year of service.

To Find:- Starting salary, Rate of annual increment, Salary at his time of retirement.

Solution:-

As we know, In A.P.

⇒ $t_{n}$ = a +(n-1) d, where $t_{n}$ = last term, a = first term,

                                       n = total number of terms,

                                       d = common difference

So,

⇒ 40,000 = a + (11-1) d

⇒ 40, 000 = a + 10d   ---------------- (1)

and,

⇒ 76,000 = a + (29-1) d

⇒ 76,000 = a + 28d   ----------------(2)

Now, multiplying eq(1) by 28 and eq(2) by 10.

                              11,20,000 = 28a + 280d  ------(3)

                              7,60,000 = 10a + 280d  -------(4)

Now, Substracting eq(4) from eq(3)

⇒ 11,20,000 - 7,60,000 = 28a - 10a + 280d - 280d

⇒ 3,60,000 = 18a

⇒ a = 20,000

Now, putting a = 20,000 in eq(1), we get

⇒ 40,000 = 20,000 + 10d

⇒ 10d = 40,000 - 20,000

⇒ d = $\frac{20,000}{10}$

⇒ d = 2,000

∵ a = 20,000 and d = 2,000

∴ His starting salary was Rs. 20,000.

Rate of annual increment ⇒ 20, 000 × $\frac{rate}{100}$ = 2,000

                                           ⇒ rate = $\frac{2,000}{200}$

                                           ⇒ rate = 10%

Now, his salary at the time of retirement will be

= 20,000 + (36-1) 2,000

= 20,000 + 35 × 2000

= 20,000 + 70,000

= 90,000

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