Question

The present income of Rahul is Rs.3675 per month. If Rahul's annual income increases by 5% every year, and the ratio of the annual incomes of Rahul and Vijay two years ago was 8:9, What was Vijay's monthly income 2 years ago?
1. 3750
2. 45000
3. 3900
4. 46250
5. 3625

Answer 1

Correct Answer - Option 1 : 3750

Given:

The present monthly income of Rahul = Rs. 3675

Rahul's annual income increases by 5% every year

The ratio of the annual incomes of Rahul and Vijay two years ago = 8:9

Formula Used:

New income = [(100 + income increment percentage)/100] × Present Income

Calculation:

Assume Rahul's annual income 2 years ago = x

and Vijay's annual income 2 years ago = y

∵ Rahul's annual increment in income= 5%,

Rahul's annual income today = [(100 + 5)/100]² × x

Also, Rahul annual income today = Rs. 3675 × 12 = Rs.44100

We can obtain Rahul's annual income, two years ago

[(100 + 5)/100]2 × x = 44100

⇒ (441/400) × x = 44100

⇒ x = 40000

∵ The ratio of the annual incomes of Rahul and Vijay two years ago = 8:9,

We can obtain Vijay's annual income, two years ago, as:

x/y = 8/9

⇒ 40000/y = 8/9

⇒ y = 45000

Vijay's monthly income two years ago is obtained as:

45000/12 = Rs.3750

∴ Vijay's monthly income two years ago was Rs.3750

Mistake Point:

It is important to note here that we have been asked Vijay's monthly income two years ago, and not his annual income two years ago. If a candidate considers the annual income two years ago as the answer, then Rs.45000 would be the answer; which would be the wrong answer for this question.