Question : A sum becomes Rs.15,500 in 7 years on simple interest at the rate of 30 percent per annum. What is the total interest for the 7 years?
Option 1: Rs. 12,200
Option 2: Rs. 1,47,000
Option 3: Rs. 10,500
Option 4: Rs. 11,500
Correct Answer: Rs. 10,500
Solution : Given, Sum= Rs. 15500
Rate of interest (r) = 30% per annum
Time (t) = 7 years
Let the principal be P.
⇒ [P + (simple interest)] = sum
⇒ [P + $\frac{\text{Prt}}{100}$] = sum
⇒ [P + $\frac{\text{P} × 30 × 7}{100}$] = 15500
⇒ [P + $\frac{\text{P} × 210}{100}$] = 15500
⇒ [P + $\frac{\text{21P}}{10}$] = 15500
⇒ $\frac{31\text{P}}{10}$ = 15500
⇒ P = $15500 × \frac{10}{31}$
⇒ P = 5000
Simple interest = 15500 – 5000 = Rs. 10500
Hence, the correct answer is Rs. 10500.
Answer laterQuestion : The total cost of a dishwasher and a vacuum cleaner was INR 78,750. The vacuum cleaner was sold at a profit of 37% and the dishwasher at a loss of 23%. If the selling price was the same for both items, then the cost price of the cheaper item was:
Option 1: INR 51,375
Option 2: INR 29,375
Option 3: INR 30,750
Option 4: INR 28,335
Correct Answer: INR 28,335
Solution : Let the cost price of the dishwater and vacuum cleaner be INR $y$ and INR $x$, respectively.
Total cost price of a dishwasher and a vacuum cleaner = INR 78,750
$x$ + $y$ = $78750$-------------------(i)
Profit of vacuum cleaner = 37% of $x$ = $0.37x$
Selling price of vacuum cleaner = $x$ + $0.37x$ = $1.37x$
Also, the loss of dishwasher = 23% of $y$ = $0.23y$
So, selling price of dishwasher = $y$ – $0.23y$ = $0.77y$
Since both have the same selling price,
⇒ $1.37x = 0.77y$
From equation (i),
⇒ $1.37(78750-y) = 0.77y$
⇒ $2.14y =107887.5$
⇒ $y$ = INR $50414.7 $
So, $x=78750-y= 78750-50414.7=28335.3$ = INR 28,335 approx
⇒ Since the vacuum cleaner is less expensive than the dishwasher.
Hence, the correct answer is INR 28,335.
Question : $x$ does $\frac{1}{4}$ of a job in 6 days. $y$ completes the rest of the job in 12 days. Then $x$ and $y$ could complete the job together in:
Option 1: $9$ days
Option 2: $9\frac{3}{5}$ days
Option 3: $8\frac{1}{8}$ days
Option 4: $7\frac{1}{3}$ days
Correct Answer: $9\frac{3}{5}$ days
Solution : Time taken by $x$ to complete $\frac{1}{4}$ of a job = 6 days
Time taken by $x$ to complete whole work = 6 × 4 = 24 days
Part of work done by $x$ in a day = $\frac{1}{24}$
Time taken by $y$ to complete $\frac{3}{4}$ of a job = 12 days
Time taken by $y$ to complete whole work = $\frac{12 × 4}{3}$ = 16 days
Part of work done by $y$ in a day = $\frac{1}{16}$
Part of work done by $x$ and $y$ in a day = $\frac{1}{24}$ + $\frac{1}{16}$ = $\frac{4 + 6}{96}$ = $\frac{10}{96}$
Time taken by $x$ and $y$ together to complete whole work = $\frac{96}{10}$ = $9\frac{3}{5}$ days
Hence, the correct answer is $9\frac{3}{5}$ days.
Question : Select the most appropriate ANTONYM of the word "established" from the given sentence:
Siben feels great satisfaction and gratified when he finds his pupils established successfully in the society when a lot have been displaced because of several failed attempts.
Option 1: displaced
Option 2: fail
Option 3: gratified
Option 4: pupils
Correct Answer: displaced
Solution : The right option is the first option.
Established implies being settled, well-founded, or having achieved success, while displaced means being removed, unsettled, or forced to leave a place, which is its antonym in this context.
So, the meanings of the other given words are:
- Fail means to be unsuccessful or to not achieve the desired objective.
- Gratified means to be pleased or satisfied as a result of achieving or fulfilling something.
- Pupil refers to a student or a learner, especially in a school or educational setting.
So, the most appropriate antonym of established is displaced.
Question : If $\sqrt{11-3 \sqrt{8}}=a+b \sqrt{2}$, then what is the value of (2a + 3b) ?
Option 1: 7
Option 2: 9
Option 3: 3
Option 4: 5
Correct Answer: 3
Solution : Given: $\sqrt{11-3 \sqrt{8}}=a+b \sqrt{2}$
⇒ $\sqrt{11-3 \sqrt{2\times2\times2}}=a+b \sqrt{2}$
⇒ $\sqrt{9+2-2×3\sqrt{2}}=a+b \sqrt{2}$
⇒ $\sqrt{(3)^2+(\sqrt2)^2-2\times3\sqrt{2}}=a+b \sqrt{2}$
⇒ $\sqrt{(3-\sqrt{2})^2}=a+b \sqrt{2}$
⇒ $3-\sqrt{2}=a+b \sqrt{2}$
Comparing both sides, we get, $a=3,b=-1$
Now, $(2a+3b)$
= $(2\times3+3\times(-1))$
= $3$
Hence, the correct answer is 3.
Question : Select the most appropriate option that can substitute the underlined segment in the given sentence.
He was looking into his book for the last two hours but couldn't find it.
Option 1: looking down on his book
Option 2: looking above his book
Option 3: looking for his book
Option 4: looking after his book
Correct Answer: looking for his book
Solution : The correct choice is the third option.
In this context, looking for is the correct phrase to convey the idea of searching for his book. The preposition for is used with the verb looking to indicate the purpose or direction of the action whereas "looking into" means to investigate.
Therefore, the correct sentence is: He was looking for his book for the last two hours but couldn't find it.
Question : A shopkeeper sold an item at 10% loss after giving a discount equal to half the marked price. Then the cost price is:
Option 1: $\frac{1}{9}$th of the marked price
Option 2: $\frac{4}{9}$th of the marked price
Option 3: $\frac{5}{9}$th of the marked price
Option 4: $\frac{7}{9}$th of the marked price
Correct Answer: $\frac{5}{9}$th of the marked price
Solution : Let the marked price = $p$ and the cost price = $q$
According to the question,
∴ 50% of $p$ = 90% of $q$
⇒ $\frac{p×50}{100}=\frac{q×90}{100}$
∴ $q=\frac{5}{9}p$
So, the cost price is $\frac{5}{9}$th of the marked price.
Hence, the correct answer is $\frac{5}{9}$th of the marked price.
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer.
Our flight was _____from Jaipur to Agra airport.
Option 1: Shifted
Option 2: diverted
Option 3: reverted
Option 4: deflected
Correct Answer: diverted
Solution : The correct word to fill in the blank is the second option.
It means to change the direction or route of something. In the context of the sentence, "diverted" is the most suitable choice because it accurately conveys the idea that the flight's route was changed from its original destination (Jaipur) to Agra airport.
The meanings of the other options are as follows:
Shifted: It means moving or transferring something from one place to another.
Reverted: It means returning to a previous state or condition.
Deflected: It means changing the direction of something by turning it aside.
Therefore, the correct sentence is, "Our flight was diverted from Jaipur to Agra airport."
Question : The least number which should be added to 8961 to make it exactly divisible by 84 is:
Option 1: 27
Option 2: 57
Option 3: 141
Option 4: 107
Correct Answer: 27
Solution : When 8961 is divided by 84, the quotient is 106, and the remainder is 57.
The required number which should be added = Divisor $-$ remainder
= 84 $-$ 57 = 27
Hence, the correct answer is 27.
Question : X is directly proportional to the square of Y. When X is 12, then Y is 2. Find the value of X when Y is 3.
Option 1: 30
Option 2: 9
Option 3: 27
Option 4: 18
Correct Answer: 27
Solution : $X\propto Y^2⇒ X = kY^2$
⇒ $\frac{\mathrm{X{_1}}}{\mathrm{Y^2{_1}}} = \frac{\mathrm{X{_2}}}{\mathrm{Y^2{_2}}} $
⇒ $\frac{12}{2^2} = \frac{\mathrm{X{_2}}}{3^2}$
⇒ $\mathrm{X{_2}} = \frac{12}{4}\times 9$
⇒ $\mathrm{X{_2}} = 27$
Hence, the correct answer is 27.
