Mr. Vishnu has an initial investment of… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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Mr. Vishnu has an initial investment of Rs.80,000 in an investment plan. After 3 years, it has grown to Rs.1,00,000, then his rate of return is

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

A
30%
B
25%
C
20%
D
10%

Did you get this right?

Solution

Student A can solve 50% of problems, so P(A solves) = $\frac{1}{2}$

Student B can solve 25% of problems, so P(B solves) = $\frac{1}{4}$

Student C can solve 20% of problems, so P(C solves) = $\frac{1}{5}$

To find the probability that at least one of them solves the problem, use the complement approach:

P(at least one solves) = 1 − P(none solve)

The probability that each student fails to solve the problem:

P(A fails) = $1 - \frac{1}{2}$

$= \frac{1}{2}$

P(B fails) = $1 - \frac{1}{4}$

$= \frac{3}{4}$

P(C fails) = $1 - \frac{1}{5}$

$= \frac{4}{5}$

Since the students work independently:

P(all fail) = P(A fails) × P(B fails) × P(C fails)

$= \frac{1}{2} \times \frac{3}{4} \times \frac{4}{5}$

$= \frac{12}{40}$

$= \frac{3}{10}$

P(at least one solves) = $1 - P(\text{all fail})$

$= 1 - \frac{3}{10}$

$= \frac{7}{10}$

Therefore, the probability that at least one of them will solve the problem is $\frac{7}{10}$ .

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