Staff Selection Commission Combined Graduate Level Exam
Question : 15 men can finish a piece of work in 40 days. The number of days after which 5 men should leave the work so that the work is finished in 45 days altogether is:
Option 1: 10
Option 2: 20
Option 3: 30
Option 4: 35
Correct Answer: 30
Solution : Given: 15 men can finish a piece of work in 40 days. Number of men to leave the work = 5 Let after $x$ number of days, 5 men left. As per given condition, $\frac{M_{1}D_{1}}{W_1}=\frac{M_{2}D_{2}}{W_2}$ $\frac{15\times (40-x)}{\text{Remaning work}}=\frac{10\times (45-x)}{\text{Remaning work}}$ ⇒ $120 - 3x =
Question : Directions: Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 16 : 8 :: 36 : 12 :: 64 : ?
Option 1: 24
Option 2: 18
Option 3: 16
Option 4: 20
Correct Answer: 16
Solution : Given: 16 : 8 :: 36 : 12 :: 64 : ?
Divide the first, third, and fourth numbers by the consecutive natural numbers to get the second, fourth, and sixth numbers – Like in, 16 : 8→16 ÷ 2 = 8 And in,
Question : A water tap fills a tub in '$p$' hours and a sink at the bottom empties it in '$q$' hours. If $p < q$, both tap and sink are open, and the tank is filled in '$r$' hours, then:
Option 1: $\frac{1}{r}$ = $\frac{1}{p}+\frac{1}{q}$
Option 2: $\frac{1}{r}$ = $\frac{1}{p}-\frac{1}{q}$
Option 3: $r = p + q$
Option 4: $r = p - q$
Correct Answer: $\frac{1}{r}$ = $\frac{1}{p}-\frac{1}{q}$
Solution : Given: A water tap fills a tub in '$p$' hours and a sink at the bottom empties it in '$q$' hours where $p < q$. So, in 1 hour the tap will fill $\frac{1}{p}$ part of the tub. Also, in 1 hour the
Question : The radii of the ends of a frustum of a cone 7 cm high are 5 cm and 3 cm. Find its volume correct to one decimal place. (Use $\pi=\frac{22}{7}$)
Option 1: 345.6 cm3
Option 2: 359.3 cm3
Option 3: 379.3 cm3
Option 4: 369.3 cm3
Correct Answer: 359.3 cm3
Solution : Given, a bigger radius, $R$ = 5 cm Smaller radius, $r$ = 3 cm Height, $h$ = 7 cm Volume of frustum = $\frac{1}{3}\pi(R^2+Rr+r^2)h$ = $\frac{1}{3}\times\frac{22}{7}\times(5^2+5\times 3+3^2)\times 7$ = $\frac{1}{3}\times 22\times 49$ = 359.3 Hence, the correct answer is 359.3 cm3.
Question : Parts of the following sentence have been given as options. Select the option that contains a grammatical error.
There was no denying the fact / that King Lear confided to / his daughter Cordelia / more than anybody else.
Option 1: that King Lear confided to
Option 2: There was no denying the fact
Option 3: more than anybody else.
Option 4: his daughter Cordelia
Correct Answer: that King Lear confided to
Solution : The error lies in the first option.
Here, confided to should be replaced with confided in,as confided is followed by the preposition to.
Therefore, the correct sentence is: There was no denying the fact that King Lear confided in his daughter
Question : When a number is increased by 216, it becomes 140% of itself. What is the number?
Option 1: 540
Option 2: 756
Option 3: 450
Option 4: 675
Correct Answer: 540
Solution : Given: When a number is increased by 216, it becomes 140% of itself. Let the number be 100%. Becoming 140% of itself means increasing by 40% Here, 40% is equivalent to 216 ⇒ 100% is equivalent to ($\frac{216}{40}$ × 100) = 540 Hence, the correct
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error".
You are required to give an explanation for your conduct within two days of the receipt of this letter.
(1) No Error
(2) for your conduct
(3) withing two days of the receipt of this letter
(4) You are required to give an explanation
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 3
Solution : The word "withing" is a spelling mistake; the correct word should be "within" to indicate a specific time frame.
Therefore, the corrected sentence is, "You are required to give an explanation for your conduct within two days of the receipt of this letter."
Question : According to Raghav, his weight is more than 64 kg but less than 74 kg. His sister does not agree with Raghav and she thinks that his weight is more than 60 kg but less than 69 kg. His mother's view is that his weight cannot be more than 68 kg. His father's view is that his weight cannot be more than 67 kg. If all are them are correct in their estimation, then what is the average of different probable weights of Raghav measured (in kg)?
Option 1: 66
Option 2: 67
Option 3: 68
Option 4: 65
Correct Answer: 66
Solution : Let $x$ be the weight of Raghav. According to Raghav, $64 < x < 74$ -----------(i) According to his sister, $60 < x < 69$ ---------(ii) According to his father, $x \leq 67$ --------(iii) According to his mother, $x \leq 68$ --------(iv) Taking the intersection
Question : If the arithmetic mean of $3a$ and $4b$ is greater than 50, and $a$ is twice $b$, then the smallest possible integer value of $a$ is:
Option 1: 20
Option 3: 21
Option 4: 19
Correct Answer: 21
Solution : According to the question, $\frac{3a+4b}{2}>50$ $\Rightarrow3a+4b>100$ $\Rightarrow3a+\frac{4a}{2}>100 (\because a = 2b)$ $\Rightarrow3a+2a>100$ $\Rightarrow5a>100$ $\Rightarrow a>20$ $\therefore$ Minimum value of $a = 21$ Hence, the correct answer is 21.
Question : The difference between the cubes of two given natural numbers is 6272, while the positive difference between the two given numbers is 8. What is the product of the two given numbers?
Option 1: 160
Option 2: 240
Option 3: 200
Option 4: 320
Correct Answer: 240
Solution : Let the numbers be x and y. So, x3 – y3 = 6272 and (x – y) = 8 Cubing both sides of the given expression, (x – y) = 8, ⇒ (x – y)3 = 83 ⇒ x3 –
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