Correct Answer: (B) 20

Explanation:

1. Define Variables:

– Let the work rate of B be r (work units per day).
– Since A’s capacity is three times more than B’s, the work rate of A is 3r.

2. Combined Work Rate:

– Together, A and B have a combined work rate of 3r + r = 4r.

3. Total Work:

– If A and B together complete the work in 15 days, the total work W can be expressed as:
W = Combined Rate × Time = 4r × 15 = 60r

4. Work Rate of A Alone:
– The work rate of A alone is 3r.
– To find the time T A alone takes to complete the work:

T = W / A’s Rate = 60r / 3r = 20 days

Answer: (B) 20

Correct Answer: (D) 33.33%

Explanation:

1. Given:
– The cost price (CP) of 40 oranges is equal to the selling price (SP) of 30 oranges.
– We need to find the percentage profit.

2. Let’s Assume:
– Let the cost price per orange be C.
– Therefore, the total cost price for 40 oranges is 40C.
– Let the selling price per orange be S.
– Therefore, the total selling price for 30 oranges is 30S.

3. Setting Up the Equation:
40C = 30S
⇒ S = 40C / 30 = 4C / 3

4. Calculating Profit:
– Profit per orange is:
S – C = (4C / 3) – C = (4C – 3C) / 3 = C / 3
– Profit Percentage is:
(Profit / Cost Price) × 100% = (C / 3) / C × 100% = (1 / 3) × 100% ≈ 33.33%

Answer: (D) 33.33%

The correct answer is: (A) 3 times

Explanation:

– Original area = s^2

– New side length = 2s, so new area = (2s)^2 = 4s^2

– Increase in area = 4s^2 – s^2 = 3s^2

Thus, the area increases by 3 times.

The correct answer is: (B) Standard deviation

Explanation:

1. Median: The median is the middle value of a data set when arranged in order. If a constant number is added to all the scores, the position of the middle value remains the same, but the value itself will increase by the constant. Hence, the median changes.

2. Standard deviation: The standard deviation measures the spread or dispersion of the data around the mean. Adding a constant to all the scores shifts the entire data set by that constant, but it does not affect the spread of the data. Therefore, the standard deviation remains unchanged.

3. Mean: The mean is the average of all the scores. If a constant is added to all the scores, the total sum of the scores increases by that constant multiplied by the number of scores, which in turn increases the mean. Hence, the mean changes.

4. Mode: The mode is the most frequently occurring value in a data set. If a constant is added to all the scores, the most frequent value will also increase by that constant. Hence, the mode changes.

Thus, the standard deviation is the only measure that does not change when a constant is added to all the scores in a series.

Correct Answer: (D) It quadruples

Explanation:

The area of a circle is given by the formula:

Area = π r^2

Where r is the radius of the circle. If the radius is doubled, the new radius becomes 2r. Substituting this into the formula for the area:

New Area = π (2r)^2 = π (4r^2) = 4 × (π r^2)

This shows that the new area is 4 times the original area. Therefore, when the radius is doubled, the area quadruples.

Thus, the correct answer is (D) It quadruples.

Correct Answer: (A) 2737

To determine how 13 is related to 2190 and apply the same relationship to 14, let’s explore possible patterns:

1. Cubing Relationship:

– 13^3 = 2197

– 2197 – 7 = 2190

It appears that 2190 is 7 less than the cube of 13.

2. Applying the Same Pattern to 14:

– 14^3 = 2744

– 2744 – 7 = 2737

Following the same logic, 14 would relate to 2737.

Answer: (A) 2737

Correct Answer: (C) He is too rich to starve.

Explanation:

– (A) He is rich enough to starve: Incorrect. This implies that being rich makes him capable of starving, which is illogical.

– (B) He is too rich and he starve: Incorrect. The grammar is wrong (“he starve” should be “he starves”), and the sentence doesn’t make sense.

– (C) He is too rich to starve: Correct. This means that his wealth prevents him from being in a situation where he would starve. The structure “too…to” is used correctly here.

– (D) He is too rich not to starve: Incorrect. This implies that being rich causes him to starve, which is contradictory and illogical.

Thus, the correct sentence is “He is too rich to starve.”

Correct Answer: (A) Neither

Explanation:

The sentence implies that none of the boys were in the playground. The word “neither” is used to indicate that not one of the two (or more) options is applicable.

– Neither: Correct, as it means “not one or the other.”

– Either: Incorrect, as it implies one of the two options is true.

– Every: Incorrect, as it refers to all members of a group individually, which doesn’t fit the context.

– All: Incorrect, as it refers to the entire group collectively, which contradicts the meaning of the sentence.

Thus, the correct answer is “Neither one of the boys was in the playground.”

Correct Answer: (D) Though; yet

Explanation:

The sentence requires a pair of conjunctions that contrast the two clauses. “Though” introduces the idea that he worked hard, and “yet” shows the contrasting result that he still failed. This pairing is grammatically correct and conveys the intended meaning of contrast effectively.

Other options:

– (A) “Hardly; when” is incorrect because it is used to indicate two events happening almost simultaneously, not contrast.

– (B) “Other; than” is incorrect because it does not fit the context of the sentence.

– (C) “No sooner; than” is used to indicate one event happening immediately after another, not contrast.

Thus, the correct answer is (D) Though; yet.

The correct answer is: (A) Obliterate

Explanation:

– Obliterate means to destroy something completely or erase it from existence. This is the correct spelling of the word.

– Obleturate, Obleterate, and Obliterait are all incorrect spellings and do not exist in the English language.

Thus, the correctly spelt word is Obliterate (A).