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SSC CHSL Tier 1 2025 17 Nov Shift 2nd

Verified by Ajay Kumar

25 questions · Choose an option, then open the answer and solution when you are ready.

Question 51

A trader sells two articles at ₹960 each. On one, he gains 20%, and on the other, he loses 20%. What is his overall profit or loss percentage?

5% Profit
4% Loss
4% Profit
5% Loss

Answer: B

Solution

Overall loss percentage = \(20^2/100 = 4\%\). Therefore, the overall loss is 4%.

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Question 52

A vase has a marked price of Rs. 550. Simran pays Rs. 350 for it because she got 2 successive discounts, one of 20% and the other of:

21%
22%
19.25%
20.45%

Answer: D

Solution

Price after the first discount = \(550 \times 80/100 = 440\). Second discount = \(440 - 350 = 90\). Second discount percentage = \(90/440 \times 100 \approx 20.45\%\).

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Question 53

A seller marks his goods 32% above their cost price but allows a 16% discount for cash payment. His percentage of profit when sold in cash is:

9.12%
8.25%
10.88%
11.5%

Answer: C

Solution

Let the cost price be 100. Marked price = \(100 \times 132/100 = 132\). Selling price after discount = \(132 \times 84/100 = 110.88\). Profit percentage = 10.88%.

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Question 54

A company had 4 departments with an average of 45 employees each. Later, a fifth department was added with 90 employees. Due to restructuring, 10 employees from each of the original four departments were transferred to the new department. What is the new average number of employees per department?

Answer: C

Solution

Total employees = \(4 \times 45 + 90 = 270\). New average = \(270/5 = 54\).

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Question 55

A savings scheme offers compound interest annually. A woman deposits ₹10,000. At the end of the first year, the interest rate is 10%. In the second year, due to inflation, the interest rate rises to 12.5%, and in the third year, it drops to 8%. Calculate the total interest she earned at the end of 3 years.

₹3,265
₹3,365
₹3,285
₹3,460

Answer: B

Solution

Final amount = \(10000 \times 1.10 \times 1.125 \times 1.08 = 13365\). Total interest = \(13365 - 10000 = 3365\). The total interest is ₹3,365.

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Question 56

What is the square of 129?

16541
16641
16741
16841

Answer: B

Solution

Using \((a-b)^2 = a^2 - 2ab + b^2\), \(129^2 = (130-1)^2 = 16900 - 260 + 1 = 16641\).

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Question 57

A perfect square between 50 and 70 is:

Answer: C

Solution

The perfect square is \(8^2 = 64\), which lies between 50 and 70.

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Question 58

A and B started a business with investments of ₹5000 and ₹4000, respectively. After 6 months, A added ₹1000 and B added ₹x. If the profit ratio is 11:18, find x.

₹9000
₹10000
₹12000
₹14000

Answer: B

Solution

A's investment-time = \(5000 \times 6 + 6000 \times 6 = 66000\). B's investment-time = \(4000 \times 6 + (4000+x) \times 6 = 48000 + 6x\). Using the profit ratio \(11:18\), \(66000/(48000+6x)=11/18\). Solving gives \(x=10,000\)₹.

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Question 59

A started a business with ₹30,000. B joined after 5 months with ₹40,000. At the end of the year, the total profit was ₹80,000. What is the share of A?

₹40000
₹42000
₹45000
₹49000

Answer: C

Solution

A's investment-time = \(30000 \times 12 = 360000\). B's investment-time = \(40000 \times 7 = 280000\). Profit ratio = \(9:7\). A's share = \(80000 \times 9/16 = 45000\). A's share is ₹45,000.

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Question 60

A, B, and C start a business. A invests ₹5000 for 12 months, B ₹4000 for 9 months, and C ₹3000 for 6 months. If the total profit is ₹380000, find A's profit share.

₹2500000
₹200000
₹2600000
₹2700000

Answer: B

Solution

Investment-time ratio = \(5000 \times 12 : 4000 \times 9 : 3000 \times 6 = 10:6:3\). A's share = \(380000 \times 10/19 = 200000\). A's profit share is ₹200,000.

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Question 61

A circular iron plate of radius 24 cm is heated, and its radius increases by 1.8%. What is the approximate percentage increase in its area?

1.8%
2.2%
3.64%
4.3%

Answer: C

Solution

Percentage increase in area = \(2r + r^2/100\), where \(r=1.8\). Thus, increase = \(2 \times 1.8 + (1.8)^2/100 = 3.6324\%\), approximately 3.64%.

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Question 62

If x + y = 6 and x² + y² = 20, then find the value of (x⁴ + x²y² + y⁴).

Answer: B

Solution

Using \((x+y)^2=x^2+y^2+2xy\), \(36=20+2xy\), so \(xy=8\). Required value = \((x^2+y^2)^2-x^2y^2=20^2-8^2=336\).

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Question 63

If (6m − 5n)² = 7 and 30mn = 60, then find the value of (6m + 5n)² + 16mn.

Answer: C

Solution

Given \(30mn=60\), so \(mn=2\). Using \((a+b)^2=(a-b)^2+4ab\), \((6m+5n)^2=7+120mn=7+240=247\). Required value = \(247+16 \times 2=279\).

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Question 64

If secx − tanx = 1/√3, then the value of secx × tanx is:

2/3
4/√3
2/√3
4/3

Answer: A

Solution

Using \((secx-tanx)(secx+tanx)=1\), \(secx+tanx=\sqrt{3}\). Adding and subtracting the equations gives \(secx=2/\sqrt{3}\) and \(tanx=1/\sqrt{3}\). Therefore, \(secx \times tanx=2/3\).

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Question 65

If x = 7sin A + 24cos A and y = 7cos A − 24sin A, then what is the value of 3(x² + y²)?

1760
2120
1875
1290

Answer: C

Solution

On squaring and adding, the cross terms cancel. Thus, \(x^2+y^2=49(\sin^2 A+\cos^2 A)+576(\sin^2 A+\cos^2 A)=49+576=625\). Therefore, \(3(x^2+y^2)=3 \times 625=1875\).

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Question 66

A man pulls a rope tied to a flagpole at ground level. The rope is 20 meters long and makes an angle of 60° with the ground. How high up the flagpole is the point where the rope is tied? Also, find the horizontal distance between the man and the base of the flagpole.

9.55 meters and 15 meters
11.45 meters and 16 meters
17.32 meters and 10 meters
12.88 meters and 19 meters

Answer: C

Solution

Height = \(20 \sin 60^\circ = 20 \times \sqrt{3}/2 \approx 17.32\) meters. Horizontal distance = \(20 \cos 60^\circ = 20 \times 1/2=10\) meters.

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Question 67

An amount of Rs. 'z' is invested in two different schemes—one offers simple interest at 13% p.a. for 4 years, and the other offers compound interest at 12% p.a. compounded annually for 2 years. If the total amount from the simple interest scheme exceeds the compound interest scheme by Rs. 78, then find the value of z.

Rs. 287
Rs. 293.66
Rs. 245.5
Rs. 299.88

Answer: B

Solution

Simple-interest amount = \(z(1+13 \times 4/100)=1.52z\). Compound-interest amount = \(z(1.12)^2=1.2544z\). Therefore, \(1.52z-1.2544z=78\), so \(z=78/0.2656\approx293.67\). The marked option is Rs. 293.66.

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Question 68

A sum of Rs. 7,500 is invested in a scheme offering r% compound interest for 2 years. Find the value of 'r' if the difference in the simple interest and compound interest for the same amount at the same rate of interest after 2 years is Rs. 108.

Answer: C

Solution

For 2 years, \(CI-SI=P(r/100)^2\). Therefore, \(108=7500(r/100)^2\). Hence, \(r^2=144\), so \(r=12\%\).

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Question 69

Gaurav invested Rs. 'x' in a scheme offering 10% compound interest for three years. Prem invested Rs. 18,000 in a scheme offering 15% simple interest for four years. Find the interest earned by Gaurav if the interest earned by Prem is Rs. '2x − 1,200'.

Rs. 1,215
Rs. 1,779
Rs. 1,560
Rs. 1,986

Answer: D

Solution

Prem's simple interest = \(18000 \times 15 \times 4/100=10800\). Given \(2x-1200=10800\), so \(x=6000\). Gaurav's compound interest = \(6000[(1.10)^3-1]=1986\). The interest earned is Rs. 1,986.

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Question 70

The sum of three numbers is 144. If the numbers are in a ratio of 3:4:5, find the smallest number.

Answer: A

Solution

Total ratio parts = \(3+4+5=12\). One part = \(144/12=12\). Smallest number = \(3 \times 12=36\).

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Question 71

Box A, contains tea worth Rs. 350 per kg and in box B contains tea worth Rs. 450 per kg. If both box A and B are mixed in the ratio 4:6 then the price of the mixture per kg is approximately:

400/-
350/-
410/-
440/-

Answer: C

Solution

Mixture price = \((350 \times 4 + 450 \times 6)/(4+6)=(1400+2700)/10=410\). The mixture costs Rs. 410 per kg.

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Question 72

A recipe for a cake calls for 2 cups of milk and 3 cups of flour. With this recipe, a cake was baked using 12 cups of flour. How many cups of milk were required?

7 cups
9 cups
8 Cups
10 Cups

Answer: C

Solution

Milk-to-flour ratio = \(2:3\). Milk required = \(12 \times 2/3=8\) cups.

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Question 73

Train 'P' can cross a pole in 8 seconds, while train 'Q' takes 15 seconds to cross train 'P' when they travel in opposite directions on parallel tracks. If the ratio of length of train 'P' to train 'Q' is 2:3 and the speed of train 'P' is 54 km/h, then find the speed (in km/h) of train 'Q'.

28 km/h
12 km/h
22 km/h
18 km/h

Answer: D

Solution

Speed of P = \(54 \times 5/18=15\) m/s. Length of P = \(15 \times 8=120\) m. Length of Q = \(120 \times 3/2=180\) m. Relative speed = \((120+180)/15=20\) m/s. Speed of Q = \(20-15=5\) m/s = \(5 \times 18/5=18\) km/h.

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Question 74

A thief is 2,000 metres ahead of a policeman when the policeman starts a chase by running at 20 m/s. If the thief is running at 12 m/s, then find the time taken by the policeman to catch the thief.

210 seconds
280 seconds
250 seconds
220 seconds

Answer: C

Solution

Relative speed = \(20-12=8\) m/s. Time = \(2000/8=250\) seconds.

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Question 75

An item undergoes two successive discounts: 12.5% (i.e., 1/8) and then 20%. After those discounts, a tax of 18% is applied on the reduced price, and the final amount the customer pays is ₹927. What was the original price of the item? (Give exact value and a rounded amount to two decimal places)

Rs. 1022.28
Rs. 1028.22
Rs. 1128.22
Rs. 1122.28

Answer: D

Solution

Let the original price be P. Final amount = \(P \times 7/8 \times 80/100 \times 118/100=927\). Thus, \(0.826P=927\), so \(P=927/0.826=927000/826\approx1122.28\). The original price is Rs. 1122.28.

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