Staff Selection Commission Combined Higher Secondary Level Exam
Question : Compound interest on a certain sum of money invested for 1.5 years at the rate of 10% per annum, compounded half-yearly is INR 5,044. What is the sum?
Option 1: INR 32,000
Option 2: INR 37,044
Option 3: INR 33,000
Option 4: INR 22,000
Correct Answer: INR 32,000
Solution : Given: Amount, $\mathrm{A = 5044}$ Rate of interest, $\mathrm{r = \frac{10}{2}=5}$% half yearly Period of compounding, $\mathrm{n = 2}$ Time, $\mathrm{t = 1.5}$ years Let the principal be $P$. We know that, $\mathrm{A = P \left(1 + \frac{r}{n}\right)^{nt} - P}$ $⇒\mathrm{5044 = P \left(1
Question : The length of the base of a triangle is 10 cm and its altitude from the same base is 8 cm. What is the area of the triangle?
Option 1: 30 cm2
Option 2: 40 cm2
Option 3: 50 cm2
Option 4: 80 cm2
Correct Answer: 40 cm2
Solution : Base = 10 cm Altitude = 8 cm Area = $\frac{1}{2} \times \text {base} \times \text {altitude}$ Substituting these values into the formula, we get: Area = $\frac{1}{2} × 10 × 8$ Area = $5 × 8$ Area = 40 cm2 Hence,
Question : P's income is 250 percent of Q's income and P's expenditure is 180 percent of Q's expenditure. If P's income is 400 percent of Q's expenditure, then what is the respective ratio of P's savings and Q's savings?
Option 1: 11 : 5
Option 2: 5 : 2
Option 3: 11 : 3
Option 4: 8 : 3
Correct Answer: 11 : 3
Solution : Let Q's expenditure be $x$. ⇒ P's expenditure = 180% of $x=\frac{180}{100}x=1.8x$ And, P's income = 400% of $x=4x$ ⇒ P's savings = $4x - 1.8x=2.2x$ Now, P's income = 250% of Q income ⇒ 250% of Q income = $4x$ ⇒ Q
Question : A certain sum was to be divided between A and B in the ratio 8 : 5. However, by mistake, it was divided in the ratio 5 : 8. Thus, A gets INR 300 less than his original share. Find the sum.
Option 1: INR 2,600
Option 2: INR 1,500
Option 3: INR 1,300
Option 4: INR 600
Correct Answer: INR 1,300
Solution : Let $x$ be the original amount. A gets $8x$ and B gets $5x$. By mistake A gets $5x$ and B gets $8x$. Now A gets Rs. 300 less than the original. According to the question, $8x-5x=300$ $⇒3x=300$ $⇒x = 100$ Total sum = $8x+5x$
Question : Directions: Select the option that is related to the sixth number in the same way as the first number is related to the second number and the third number is related to the fourth number. 27 : 841 :: 18 : 400 :: ? : 324
Option 1: 16
Option 2: 12
Option 3: 14
Option 4: 10
Correct Answer: 16
Solution : Given: 27 : 841 :: 18 : 400 :: ? : 324
Like, 27 : 841→(27 + 2)2 = 292 = 841 And, 18 : 400→(18 + 2)2 = 202 = 400 Similarly, follow the same pattern for 324 : ?→Let
Question : Directions: A piece of paper is folded and punched as shown below in the question figures. From the given answer figures, indicate how it will appear when opened.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : When the given paper is unfolded, it will look like –
Hence, the third option is correct.
Question : Directions: Find the total number of triangles in the given figure.
Option 1: 11
Option 3: 9
Correct Answer: 10
Solution : The given figure can be labelled as shown below –
Now, in the above figure, there are a total of 10 triangles. They are ABH, BHI, HIG, GIF, BIC, CID, DIF, DEF, GAC, GEC.
Hence, the fourth option is correct.
Question : Directions: Select the figure from the given options that can replace the question mark (?) in the following series.
Solution : According to the given question figure – 1. The arrow and small square are shaded alternatively and the arrow moves 90° in an anticlockwise direction. 2. The arc line of the circle decreases by 1 in an anticlockwise direction in each box. So, following the above
Question : A shopkeeper marked a product 40% above the cost price and sold the product for Rs. 3780 by giving a discount of 10%. The profit percentage of the shopkeeper is:
Option 1: 30%
Option 2: 26%
Option 3: 42%
Option 4: 14%
Correct Answer: 26%
Solution : Let the cost price be 100. The shopkeeper marked his goods 40% above the cost price. The marked price = 140 He then gave a 10% discount on the marked price, The selling price $=\frac{90}{100}×140=126$ Given that the selling price is Rs. 3780. So, the
Question : Sriya with her family travelled from Bolpur to Suri by car at a speed of 40 km/h and returned to Bolpur at a speed of 50 km/h. The average speed for the whole journey is:
Option 1: $44\frac{4}{9}$ km/h
Option 2: $45$ km/h
Option 3: $45\frac{1}{2}$ km/h
Option 4: $44.78$ km/h
Correct Answer: $44\frac{4}{9}$ km/h
Solution : Let denote the distance between Bolpur and Suri as $d$. The time taken to travel from Bolpur to Suri is $\frac{d}{40}$ hours and the time taken to travel back from Suri to Bolpur is $\frac{d}{50}$ hours. So, the total distance travelled is $2d$ (to
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