XAT 2019 — QA & DI Question 2
A, B, C, D and E are five employees working in a company. In two successive years, each of them got hikes in his salary as follows:
A : p% and (p + 1)%,
B : (p + 2)% and (p - 1)%,
C : (p + 3)% and (p - 2)%,
D : (p + 4)% and (p - 3)%,
E : (p + 5)% and (p - 4)%.
If all of them have the same salary at the end of two years, who got the least hike in his salary?
Answer & solution
E
- B
B
- C
D
- D
A
- E
C
Since final salary for all five employees is same, least hike will be for that employee who has the highest initial salary.
Again, since final salary for all five employees is same, initial salary will be highest for that employee who has least overall % change.
Let us calculate % change for all the employees.
We know when a number is successively increased b a% and then b%, overall % change is a + b + ab/100.
Here let us assume the value of p as 10%
Therefore, % change for
A: 10 + 11 + 10 × 11/100 = 21 + 1.1 = 22.1%
B: 12 + 9 + 12 × 9/100 = 21 + 1.08 = 22.08%
C: 13 + 8 + 13 × 8/100 = 21 + 1.04 = 22.04%
D: 14 + 7 + 14 × 7/100 = 21 + 0.98 = 21.98%
E: 15 + 6 + 15 × 6/100 = 21 + 0.90 = 21.90%
∴ Least % change is for E, hence E has the highest initial salary hence the least hike.
Hence, option (a).