NIMCET 2025 Reasoning PYQ — At an IIM entrepreneurship summit, two young founders __ Karan an… | Mathem Solvex | Mathem Solvex
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NIMCET 2025 — Reasoning PYQ
NIMCET | Reasoning | 2025
At an IIM entrepreneurship summit, two young founders __ Karan and Deepak __ introduced their startup. In their quirky opening, they said "The product of our ages is 240. And just like in our startup strategy, twice Deepak's age is 4 years more than Karans's age How old was Deepak two years ago?
Choose the correct answer:
A.
8 Years
B.
15 Years
C.
6 Years
D.
10 Years
(Correct Answer)
Correct Answer:
10 Years
Explanation
1. Formulate the equations based on the given conditions:
Condition 1 (Product of ages):
K×D=240⟹K=D240— (Eq. 1)
Condition 2 (Twice Deepak's age is 4 more than Karan's):
2D=K+4⟹K=2D−4— (Eq. 2)
2. Solve for D by equating (Eq. 1) and (Eq. 2):
D240=2D−4
240=D(2D−4)
240=2D2−4D
Divide the entire equation by 2:
D2−2D−120=0
3. Factorize the quadratic equation:
We need two numbers that multiply to −120 and add to −2. Those numbers are −12 and +10.
D2−12D+10D−120=0
D(D−12)+10(D−12)=0
(D−12)(D+10)=0
Since age cannot be negative, D=12.
4. Find Deepak's age two years ago:
Deepak's present age (D)=12 years.
Age two years ago =D−2
12−2=10
Correct Option: D) 10 years
Explanation
1. Formulate the equations based on the given conditions:
Condition 1 (Product of ages):
K×D=240⟹K=D240— (Eq. 1)
Condition 2 (Twice Deepak's age is 4 more than Karan's):
2D=K+4⟹K=2D−4— (Eq. 2)
2. Solve for D by equating (Eq. 1) and (Eq. 2):
D240=2D−4
240=D(2D−4)
240=2D2−4D
Divide the entire equation by 2:
D2−2D−120=0
3. Factorize the quadratic equation:
We need two numbers that multiply to −120 and add to −2. Those numbers are −12 and +10.
