Quants 13 - Progressions

Practice Questions:

Question 1:

Two persons—Ramu Dhobi and Kalu Mochi have joined Donkey-work Associates. Ramu Dhobi and Kalu Mochi started with an initial salary of ` 500 and ` 640 respectively with annual increments of ` 25 and ` 20 each respectively. In which year will Ramu Dhobi start earning more salary than Kalu Mochi?

The current difference between the salaries of the two is ` 140. The annual rate of reduction of this dfference is ` 5 per year. At this rate, it will take Ramu Dhobi 28 years to equalise his salary with Kalu Dhobi’s salary.

Thus, in the 29th year he will earn more.

This problem should be solved while reading and the thought process should be 140/5 = 28. Hence, answer is 29th year.

Question 2:

Find the sum of all numbers divisible by 6 in between 100 to 400.

Here 1st term = a = 102 (which is the 1st term greater than 100 that is divisible by 6.)

The last term less than 400, which is divisible by 6 is 396.

The number of terms in the AP; 102, 108, 114…396 is given by [(396 – 102)/6] +1= 50 numbers.

Common difference = d = 6

So, S = 25 (204 + 294) = 12450

Question 3:

How many terms are there in the GP 5, 20, 80, 320,… 20480?

The series would be 5, 20, 80, 320, 1280, 5120, 20480. Thus, there are a total of 7 terms in the series. 

Question 4:

The seventh term of a GP is 8 times the fourth term. What will be the first term when its fifth term is 48?

In the case of a G.P. the 7th term is derived by multiplying the fourth term thrice by the common ratio.

Since, the seventh term is derived by multiplying the fourth term by 8, the relationship r^3 = 8 must be true.

Hence, r = 2

If the fifth term is 48, the series in reverse from the fifth to the first term will look like:

48, 24, 12, 6, 3. 

The answer is 3.

Question 5:

How many natural numbers between 300 to 500 are multiples of 7?

The series will be 301, 308, …….. 497

Hence, Answer = 196/7 + 1 = 29

Time to Think:

Bobby was appointed to Mindworkzz in the pay scale of ` 7000–500–12,500. Find how many years he will take to reach the maximum of the scale.