Arithmetic and Geometric Progressions

You are here: Home  CAT Questionbank   CAT Quant  AP, GP  Question 15
Combo of Ratios and Progressions

Ratio of Amounts

The salaries earned by two friends Anil and Jeetu in different years are in A.P. If the ratio of the amount earned by them in ‘p’ number of years are (4p+1) : (2p+17). Then find the ratio of amount earned by them in the 7th year.
1. (2p+1) : (4p+6)
2. 53 : 43
3. 4 : 7
4. 15p : 36p

Choice B. 53:43

Detailed Solution

Let a1, a2 be the salaries of their first year and d1 and d2 be the difference between salaries of two consecutive years.

Now, the sum of p terms of their salaries are

Sp = $\frac{p}{2} * [2a_1 + (p-1)d_1]$

S'p = $\frac{p}{2} * [2a_2 + (p-1)d_2]$

$\frac{\frac{p}{2} * [2a_1 + (p-1)d_1]}{\frac{p}{2} * [2a_2 + (p-1)d_2]} = \frac{4p+1}{2p + 17}$

$\frac{[2a_1 + (p-1)d_1]}{[2a_2 + (p-1)d_2]} = \frac{4p+1}{2p + 17}$ -------------------- (1)

Now,
Ratio of Salaries earned by them in the 7th year

= $\frac{a_1 + 6d_1}{a_2 + 6d_2}$

= $\frac{2a_1 + 12d_1}{2a_2 + 12d_2}$ (Multiplying and Dividing by 2)

= $\frac{2a_1 + (13 - 1)d_1}{[2a_2 + (13 - 1)d_2}$

= $\frac{4 * 13 + 1}{2 * 13 + 17}$

= 53 : 43

Our Online Course, Now on Google Playstore!

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

More questions from Progressions

With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. Reinforce these ideas with these questions.