Direction: Study the following information carefully and answer the given…
2020
Direction: Study the following information carefully and answer the given questions.
Eight persons A, B, C, D, E, F, G and H are working in a company in three different departments – Production, Management and Finance on two posts – Manager and General Manager but not necessarily in the same order. All they have different ages in the whole number.
E’s age is twice of C’s age. A is 53 years old and working in production. The persons whose total age is 100 years are working in Finance as General Manager. F is working in Production. B is working in management but not with D and posts of B and D are different. Both H and G are working at same post but not in production department. Both H and F are working at different post. Not more than two persons working on same post in same department.
Both E and A working in same department but at different post. Both A and D work in different post. Sum of the ages of C and G is 64 years. Both C and D are manager but in different departments but not in the production. E is 12 years older to F and 12 years younger to H. Difference between the age of C and D is equal to H’s age. B is 30 years old and its age is half the H’s age.
How many persons are working as manager?
- A.
Four
- B.
Five
- C.
Three
- D.
Two
- E.
One
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
In an ages-with-arrangement puzzle, always lock the NUMBERS first. Every relational clue (twice of, older/younger by, half of, difference equals) is an equation; chaining them from any clue that gives an absolute value resolves all ages. Only then place people into departments and posts using the placement constraints, because several placement clues depend on the ages you just found.
Step 1 - Solve every age
Start from the two absolute anchors, B = 30 and A = 53, and chain the relations:
B is half of H, so H = 2 x 30 = 60.
E is 12 younger than H, so E = 60 - 12 = 48.
E is 12 older than F, so F = 48 - 12 = 36.
E is twice C, so C = 48 / 2 = 24.
C + G = 64, so G = 64 - 24 = 40.
Difference between C and D equals H (=60): |24 - D| = 60, and a positive whole age forces D = 84.
Final ages: A=53, B=30, C=24, D=84, E=48, F=36, G=40, H=60 - eight distinct whole numbers, as required.
Step 2 - Read off the post each person holds
Place people using the constraints; the relevant logic for the COUNT of managers:
G + H = 100, the only pair summing to 100, so both are General Managers in Finance.
H and F hold different posts, so F is a Manager.
A is in Production with E (same department, different posts); A and D have different posts, and D is a Manager, so A is a General Manager and therefore E is a Manager.
B and D have different posts; D is a Manager, so B is a General Manager.
C and D are both Managers (stated directly).
B is in Management, and C and D sit in different non-Production departments, so D cannot share Management with B - D is in Finance and C is in Management.
Step 3 - The grid
Person | Age | Department | Post |
|---|---|---|---|
A | 53 | Production | General Manager |
E | 48 | Production | Manager |
F | 36 | Production | Manager |
B | 30 | Management | General Manager |
C | 24 | Management | Manager |
D | 84 | Finance | Manager |
G | 40 | Finance | General Manager |
H | 60 | Finance | General Manager |
Cross-check
The Managers are C, D, E and F - four people. The General Managers are A, B, G and H - also four, matching the rule that no post-department cell holds more than two people. Hence the number of persons working as Manager is four.