Staff Selection Commission Combined Higher Secondary Level Exam
Question : A invests Rs. 64,000 in a business. After a few months, B joined him with Rs. 48,000. At the end of the year, the total profit was divided between them in the ratio 2 : 1. After how many months did B join?
Option 1: 8
Option 2: 4
Option 3: 6
Option 4: 7
Correct Answer: 4
Solution : Let the number of months after which B joined as $x$ months. Therefore, A's investment was for 12 months and B's investment was for $(12 - x)$ months. The ratio of A's investment to B's investment is equal to the ratio of their profits. $⇒\frac{(64000 \times 12)}{(48000 \times (12 - x)) }= \frac{2}{1}$ $⇒\frac{(4 \times 12)}{(3 \times (12 - x)) }= \frac{2}{1}$ $⇒\frac{8}{(12 - x)}= 1$ $⇒x= 12 - 8 = 4$ months Hence, the correct answer is 4.
Question : Lakshita purchased a sofa set at a discount of 25%. As per her calculations, she noticed that if she had not been given this discount, she would have paid INR 22,400 more as the cost of this sofa set. How much did Lakshita pay for the sofa set?
Option 1: INR 22,400
Option 2: INR 33,600
Option 3: INR 67,200
Option 4: INR 67,000
Correct Answer: INR 67,200
Solution : Let the marked price be $x$. Selling price after 25% discount = $x$ – 25% of $x$ = $\frac{3x}{4}$ According to the question, $x-\frac{3x}{4}$ = 22400 ⇒ $\frac{x}{4}$ = 22400 ⇒ $x$ = 89,600 Now, the price paid by Lakshita = $\frac{3x}{4}=\frac{3}{4}×89600$ = INR 67,200 Hence, the correct answer is INR 67,200.
Question : Minor arc $BC$ subtends $\angle BAC$ and $\angle BDC$ at points $A$ and $D$, respectively, on the circumference of the major sector of the circle with centre $O$. What is the value (in degrees) of $(\angle ABC+\angle ACB)$, if $\angle BDC=73^{\circ}?$
Option 1: $117^{\circ}$
Option 2: $107^{\circ}$
Option 3: $103^{\circ}$
Option 4: $113^{\circ}$
Correct Answer: $107^{\circ}$
Solution : Given: Minor arc $BC$ subtends $\angle BAC$ and $\angle BDC$ at points $A$ and $D$. $\angle BDC=73^{\circ}$ So, $\angle BAC=73^{\circ}$ (common base) We know that in $\triangle ABC$, $\angle ABC+\angle BAC+\angle ACB=180^{\circ}$ Putting the value of $\angle BAC=73^{\circ}$, we have, ⇒ $\angle ABC+73^{\circ}+\angle ACB=180^{\circ}$ ⇒ $\angle ABC+\angle ACB=180^{\circ}–73^{\circ}$ ⇒ $\angle ABC+\angle ACB=107^{\circ}$ Hence, the correct answer is $107^{\circ}$.
Question : Directions: Identify the figure given in the options which when put in place of the question mark (?) will logically complete the series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : In the given figure, the following pattern is being followed – 1. The lines with the square on the top change to the line with an asterisk on the top in every alternate box one by one, starting from the left side from the second box onwards. 2. The line with an asterisk on the bottom changes to the line with the square on the bottom in every alternate box one after the other, starting from the right side from the third box onwards.
So, following the above pattern, the required figure will be –
Hence, the second option is correct.
Question : At the beginning of a partnership business, the capital of B was $\frac{3}{2}$ times that of A. After 8 months B withdrew $\frac{1}{2}$th of his capital and after 10 months A withdrew $\frac{1}{4}$th of his capital. At the end of the year, if the profit incurred is Rs. 53,000, find the amount received by A.
Option 1: Rs. 30,800
Option 2: Rs. 32,000
Option 3: Rs. 30,000
Option 4: Rs. 23,000
Correct Answer: Rs. 23,000
Solution : Let A invest Rs. $x$ at the beginning of the partnership business, then the ratio of the profit A and B, $=(x\times10+\frac{3x}{4}\times2):(\frac{3x}{2}\times8+\frac{3x}{4}\times4)$ $=\frac{23x}{2}:15x$ $=23:30$ The amount received by A in the profit, $=\frac{23}{53}\times53000$ = Rs. 23,000 Hence, the correct answer is Rs. 23,000.
Question :
Directions: In the following question, select the related word from the given alternatives. Car : Garage :: ? : Hangar
Option 1: Train
Option 2: Truck
Option 3: Aeroplane
Option 4: Bus
Correct Answer: Aeroplane
Solution :
Given: Car : Garage :: ? : Hangar
Like, a garage is a place where cars are parked. Similarly, a hangar is a place where aeroplanes are kept.
Hence, the third option is correct.
Question : Directions: A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in two matrices, given below. The columns and rows of Matrix (I) are numbered from 0 to 4 and that of Matrix (II) are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g. 'D' can be represented by 68,10, etc and 'R' can be represented by 34, 22, etc. Similarly, you have to identify the set for the word PRIME.
Option 1: 42, 31, 20, 79, 57
Option 2: 33, 34, 11, 97, 56
Option 3: 95, 13, 02,14, 23
Option 4: 30, 22, 00, 65, 99
Correct Answer: 33, 34, 11, 97, 56
Solution : Given: PRIME
Number representations of each letter – P → 01, 30, 33, 42, 95 R → 04, 13, 22, 31, 34 I → 00, 02, 11, M → 03, 65, 79, 97 E → 24, 32, 41, 56
First option: 42, 31, 20, 79, 57; I and E cannot be represented as 20 and 57 respectively. Second option: 33, 34, 11, 97, 56; All the letters of the word PRIME can be represented through this option. Third option: 95, 13, 02,14, 23; M and E cannot be represented as 14 and 23 respectively. Fourth option:30, 22, 00, 65, 99; E cannot be represented as 99.
So, PRIME can be represented using the codes 33, 34, 11, 97, 56. Hence, the second option is correct.
Question : Select the option that will improve the underlined part of the given sentence.
Adyasha would have been looked gorgeous in ethnic apparel.
Option 1: was looked
Option 2: would have looked
Option 3: had looking
Option 4: would be looked
Correct Answer: would have looked
Solution : The correct choice is the second option.
The correct form for expressing the hypothetical situation of Adyasha not actually wearing ethnic apparel is "would have looked". This adheres to the general rule of the third conditional structure, where "would have" is followed by the past participle form of the main verb i.e., "looked".
Therefore, the correct sentence is: Adyasha would have looked gorgeous in ethnic apparel.
Question : Select the most appropriate synonym of the word 'scrutiny' from the given sentence. The company's strategic plan included a comprehensive analysis of market trends and consumer behaviour.
Option 1: behaviour
Option 2: comprehensive
Option 3: trends
Option 4: analysis
Correct Answer: analysis
Solution : The correct choice will be the fourth option.
Scrutiny means the careful and detailed examination of something in order to get information about it. Analysis denotes the result of a careful examination of something, making it a fitting synonym.
The meanings of the other words are:
Behaviour: It means the way that you act or behave.
Comprehensive: It means covering completely or broadly.
Trends: It means a general change or development.
According to the sentence, the correct synonym for scrutiny is analysis.
Question : The average of 13 results is 70. If the average of the first seven is 65 and that of the last seven is 75, the seventh result is:
Option 1: 67
Option 2: 70
Option 3: 68
Option 4: 70.5
Correct Answer: 70
Solution : The average of 13 results = 70 The sum of all results = 13 × 70 = 910 The average of the first seven = 65, and the average of the last seven = 75 The sum of the first seven results = 7 × 65 = 455 The sum of the last seven results = 7 × 75 = 525 Seventh result = sum of first seven results + sum of last seven results – the sum of all results = 455 + 525 – 910 = 70 Hence, the correct answer is 70.
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