Correct Answer: 12 years

Solution : Given:
A man was 31 years old when his son was born.

When their son was 7 years old, his wife's age = 26 years
Wife's age when the son was born = (26 – 7) = 19 years

Therefore, the difference between the man's age and his wife's age = (31 – 19) = 12 years

So, the difference between their ages is 12 years. Hence, the fourth option is correct.

Correct Answer: $2:1$

Solution : $\frac{a-b}{b-c}=\frac{1}{2}⇒2a+c = 3b$ ........(1)
$\frac{a-b}{c-d}=\frac{1}{3} ⇒3a-3b = c-d$ ........(2)
Substituting the value of $b$ from (1) in (2),
$3a-2a-c=c-d$
⇒ $a+d = 2c$
$\therefore (a + d):c = \frac{2c}{c} = 2:1$
Hence, the correct answer is $2:1$.

Correct Answer: 69 hours

Solution : Given: Robert takes twice as much time as Tom and thrice as much time as George to complete a work.
Working together, they can complete it in 23 hours.
Work = Time × Efficiency
According to the question,
$\frac{1}{x}+\frac{2}{x}+\frac{3}{x}=\frac{1}{23}$
⇒ $\frac{1+2+3}{x}=\frac{1}{23}$
⇒ $\frac{6}{x}=\frac{1}{23}$
⇒ $x=138$
The time that Tom will take to complete the work = $\frac{138}{2}=69$ hours
Hence, the correct answer is 69 hours.

Correct Answer: Telangana

Solution : The correct answer is Telangana.

The Hindu festival of Bonalu is dedicated to the adoration of Goddess Mahakali. The twin cities of Hyderabad and Secunderabad, as well as other regions of the Indian state of Telangana, commemorate this festival every year. It is observed between July and August, during Ashadha masam.

Correct Answer: Pangea

Solution : The correct answer is Pangea.

The supercontinent Pangea originated between 320 and 195 million years ago. Earth had only one enormous continent at that time, encircled by a single ocean called Panthalassa. There were no seven continents on Earth at that time.

Correct Answer: 9

Solution : In the below diagram, the shaded part represents the region common in both Junior students, good Athletes, and swimmers but not Cyclists.

So, from the above, 9 people are Junior students who are both good Athletes and swimmers but not Cyclists. Hence, the first option is correct.

Correct Answer: State correspondence

Solution : The correct answer is State correspondence.

The Diwan-i-Insha was the Department of State correspondence. These specific names were given to the different ministries during the administration of the Delhi Sultanate. The Department of Military was headed by Diwan-i-Arz. The Department of Revenue and Finance was headed by Wazir or Diwan-i-wizarat. The Department of Foreign Affairs was headed by Diwan-i-Risalat.

Correct Answer: S

Solution : Given:
K, M, O, Q, ?

Add 2 to the place value of the letters of each term to obtain the next term in the series –
K + 2 = M; M + 2 = O; O + 2 = Q; Q + 2 = S

So, S is the missing term in the series. Hence, the third option is correct.

Correct Answer: (2)

Solution : The error lies in the second part of the sentence.

The conjunction that should be used after the noun clause ("it was fortunate") to introduce the other clause in the sentence. Also, the use of the preposition "of" is not required and thus should be omitted to make the sentence grammatically accurate.

Therefore, the correct sentence is: It was fortunate that all the inmates escaped from the blazing fire.

Correct Answer: $38 \frac{10}{49} \mathrm{~h}$

Solution : Works done by two pipes in 1 hours = $\left(\frac{1}{12}+\frac{1}{16}\right)=\frac{\left(4+3\right)}{48}=\frac{7}{48}$
Time taken by the pipes to fill the tank = $\frac{48}{7}$ hr = $6\frac{6}{7}$ hr
Due to leakage time taken = $6\frac{6}{7}$ hr + 90 min = 8$\frac{5}{14}$ hr
Work done by (two pipes + leak) in 1 hours = $\frac{14}{117}$ hr
⇒ Work done by the leak in 1 hour = ($\frac{7}{48} - \frac{14}{117}$) = $\frac{49}{1872}$
⇒ Leak will empty the full as a term in = $\frac{1872}{49}$ hours
Hence, the correct answer is $39\frac{10}{49} \text{h}$.