A speaks the truth in 70% of cases and… - CUET UG 2025 General Test PYQ

CUET UG 2025 — General Test Quantitative Reasoning

2025mcqmedium

A speaks the truth in 70% of cases and B lies in 40% of cases. The probability that they will say the same thing while describing a single event (to have occurred or not) will be:

Official previous-year question

Held on 26 May 2025 · Verified 13 Jul 2026.

Options

A
$\frac{23}{50}$
B
$\frac{21}{50}$
C
$\frac{6}{50}$
D
$\frac{27}{50}$

Did you get this right?

Solution

A speaks the truth in 70% of cases, so A lies in 30% of cases.

B lies in 40% of cases, so B speaks the truth in 60% of cases.

Therefore:

P(A tells truth) = $\frac{7}{10}$
P(A lies) = $\frac{3}{10}$
P(B tells truth) = $\frac{3}{5}$
P(B lies) = $\frac{2}{5}$

For A and B to say the same thing while describing a single event, either both tell the truth or both lie.

P(Both tell truth) = P(A tells truth) × P(B tells truth)

$= \frac{7}{10} \times \frac{3}{5}$

$= \frac{21}{50}$

P(Both lie) = P(A lies) × P(B lies)

$= \frac{3}{10} \times \frac{2}{5}$

$= \frac{6}{50}$

P(They say the same thing) = P(Both tell truth) + P(Both lie)

$= \frac{21}{50} + \frac{6}{50}$

$= \frac{27}{50}$

Therefore, the probability that they will say the same thing is $\frac{27}{50}$ .

Your note

CUET UG Quantitative Reasoning in other years

Quantitative Reasoning 2024 Quantitative Reasoning 2023 Quantitative Reasoning 2022

Keep practicing Quantitative Reasoning

Work through every CUET UG Quantitative Reasoning PYQ, year by year.

Browse all General Test topics

Options

Did you get this right?

Solution

Your note

CUET UG Quantitative Reasoning in other years

More CUET UG Quantitative Reasoning questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

Geometry

Current Affairs

Keep practicing Quantitative Reasoning