SSC CHSL Tier 1 2025 18 Nov Shift 3rd

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

Question 51

If x is irrational and y is irrational, then x+y is:

  1. Always irrational

  2. Always rational

  3. Rational if x=-y

  4. Never rational

Answer: C

Solution

The sum of two irrational numbers can be rational. If x=-y, then x+y=0, which is rational.

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Question 52

In triangle ABC, AB=7 cm, BC=24 cm and AC=25 cm. Find the value of tan C + sin C + 2 cot A.

  1. 2.566

  2. 1.233

  3. 1.155

  4. 2.35

Answer: C

Solution

Since 7²+24²=25², angle B is 90°. Therefore, tan C=7/24, sin C=7/25 and cot A=7/24. The required value is 7/24+7/25+2(7/24)=1.155 approximately.

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Question 53

Sonu and Monu together can do a piece of work in 30 days. If Sonu is 20% less efficient than Monu, in how many days can Sonu, working alone, complete 40% of the work?

  1. 32 days

  2. 25 days

  3. 30 days

  4. 27 days

Answer: D

Solution

Let Monu's daily work rate be m. Sonu's rate is 0.8m. Thus, 1.8m=1/30, so Sonu's rate is 2/135 of the work per day. Time for 40% work = (2/5)/(2/135)=27 days.

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Question 54

The angle subtended by a chord at the centre is 90°. Its length is 8 cm. What is the radius?

  1. 4√2 cm

  2. 8√2 cm

  3. 6 cm

  4. 10 cm

Answer: A

Solution

Chord length = 2r sin(90°/2) = r√2. Therefore, 8=r√2, giving r=4√2 cm.

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Question 55

The length of a chord that is at a distance of 5 cm from the centre of a circle of radius 13 cm is:

  1. 12 cm

  2. 18 cm

  3. 24 cm

  4. 30 cm

Answer: C

Solution

The perpendicular from the centre bisects the chord. Half-chord = √(13²-5²)=√144=12 cm. Hence, the full chord is 24 cm.

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Question 56

The angle subtended by a chord at the centre is 120°. The angle between the chord and the tangent at one endpoint is:

  1. 30°

  2. 60°

  3. 90°

  4. 120°

Answer: B

Solution

The triangle formed by the two radii and the chord is isosceles. Each base angle is (180°-120°)/2=30°. The tangent is perpendicular to the radius, so the angle between the chord and tangent is 90°-30°=60°.

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Question 57

The ratio of the curved surface area of a cylinder to its total surface area is 7:10. If the volume of the cylinder is 12672 cm³, find its curved surface area.

  1. 2080 cm²

  2. 2348 cm²

  3. 2112 cm²

  4. 2648 cm²

Answer: C

Solution

CSA/TSA=h/(h+r)=7/10, so h=7r/3. Using πr²h=12672 and π=22/7 gives r=12 cm and h=28 cm. CSA=2πrh=2×22/7×12×28=2112 cm².

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Question 58

A circle is inscribed in triangle PQR, touching QR, PR and PQ at S, U and T respectively. PQ=(QR+5) cm and PQ=(PR+2) cm. If the perimeter of triangle PQR is 32 cm, find PR.

  1. 8 cm

  2. 11 cm

  3. 13 cm

  4. 10 cm

Answer: B

Solution

Let PR=x. Then PQ=x+2 and QR=x-3. From the perimeter, x+(x+2)+(x-3)=32, so 3x-1=32 and x=11 cm.

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Question 59

At 5% per annum simple interest, the simple interest earned by A on his investment for 4 years equals the simple interest earned by B on his investment for 6 years. If B invested ₹12,000 less than A, what was A's investment (principal)?

  1. ₹24,000

  2. ₹30,000

  3. ₹36,000

  4. ₹48,000

Answer: C

Solution

Equal simple interest gives 4A=6B, so A=1.5B. Also A-B=12000. Thus 0.5B=12000, B=24000 and A=36000.

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Question 60

In a partnership, P, Q and R invested ₹50,000, ₹60,000 and ₹70,000 respectively. If the total profit is ₹24,000, how much will Q receive?

  1. ₹7,200

  2. ₹8,000

  3. ₹8,500

  4. ₹9,000

Answer: B

Solution

The investment ratio is 50000:60000:70000=5:6:7. Q's share = 24000×6/(5+6+7)=₹8,000.

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Question 61

Two numbers are in the ratio 5:8. If 12 is added to each number, the new ratio becomes 11:17. What is the sum of the original two numbers?

  1. 412

  2. 276

  3. 350

  4. 312

Answer: D

Solution

Let the numbers be 5x and 8x. Then (5x+12)/(8x+12)=11/17. Solving gives 85x+204=88x+132, so x=24. Their sum is 13x=312.

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Question 62

What is the least value that should be added to 1812 to make it divisible by 7, 11 and 14?

  1. 12

  2. 36

  3. 72

  4. 154

Answer: B

Solution

LCM of 7, 11 and 14 is 154. Since 1812=154×11+118, the least addition is 154-118=36.

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Question 63

The sum of two numbers is 84 and their HCF is 12. If the ratio of their LCM to their HCF is 12:1, what are the two numbers?

  1. 36 and 48

  2. 24 and 60

  3. 12 and 72

  4. 42 and 42

Answer: A

Solution

The LCM is 12×12=144. Let the numbers be 12a and 12b, where HCF(a,b)=1. Then a+b=7 and ab=144/12²=1? This is inconsistent with the stated LCM ratio. The screenshot's intended answer is 36 and 48, whose HCF is 12 and LCM is 144.

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Question 64

The average of 20 numbers is 45. If each number is decreased by 7, what will be the new average?

  1. 38

  2. 40

  3. 36

  4. 34

Answer: A

Solution

When the same value is subtracted from every observation, the average decreases by that value. New average=45-7=38.

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Question 65

The average salary of employees in a company is ₹20,000. If a new employee with a salary of ₹50,000 joins, the average increases by ₹500. Find the number of employees originally in the company.

  1. 59

  2. 55

  3. 60

  4. 65

Answer: A

Solution

Let the original number be n. Then (20000n+50000)/(n+1)=20500. Solving gives 20000n+50000=20500n+20500, so n=59.

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Question 66

If A is 50% more than B, and C is 30% less than the sum of A and B, then C is what percent of A?

  1. 116.67%

  2. 125.57%

  3. 134.26%

  4. 111.14%

Answer: A

Solution

Let B=100, so A=150. Then C=70% of (150+100)=175. Thus C as a percentage of A=(175/150)×100=116.67%.

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Question 67

A train covers 100 km at a speed of 50 km/h. Due to track repair, it reduces its speed by 40% for the next 60 km. What is the total time taken for the full journey?

  1. 2 hours

  2. 4 hours

  3. 5 hours

  4. 10 hours

Answer: B

Solution

Time for the first 100 km=100/50=2 hours. Reduced speed=50×60%=30 km/h. Time for the next 60 km=60/30=2 hours. Total=4 hours.

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Question 68

18 men can complete a work in 20 days. After 10 days, 6 men leave. In how many more days will the remaining men finish the work?

  1. 12 days

  2. 13 days

  3. 14 days

  4. 15 days

Answer: D

Solution

Total work=18×20=360 man-days. Work done in 10 days=18×10=180 man-days. Remaining work=180 man-days. With 12 men, required days=180/12=15.

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Question 69

If a person purchases items worth ₹2,050 at a discount rate of 26%, what will be the total savings?

  1. ₹530

  2. ₹500

  3. ₹450

  4. ₹533

Answer: D

Solution

Savings=26% of ₹2,050=(26/100)×2050=₹533.

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Question 70

After deducting 25% from the marked price, the item's selling price is ₹7,200. If the discount is raised to 30%, what will the selling price be?

  1. ₹6,720

  2. ₹6,500

  3. ₹6,000

  4. ₹5,500

Answer: A

Solution

₹7,200 is 75% of the marked price. Marked price=7200/0.75=₹9,600. New selling price=70% of ₹9,600=₹6,720.

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Question 71

Two containers A and B hold 20 litres and 30 litres of liquid mixture, respectively. Container A has milk and water in the ratio 3:2, while container B has them in the ratio 4:1. If the entire contents are mixed, what is the resulting ratio of milk to water?

  1. 6:13

  2. 7:3

  3. 18:7

  4. 2:1

Answer: C

Solution

Container A contains 12 L milk and 8 L water. Container B contains 24 L milk and 6 L water. Total milk=36 L and water=14 L. Ratio=36:14=18:7.

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Question 72

Which is the largest among these: cube root of 2, square root of 3, and sixth root of 5?

  1. ∛2

  2. √3

  3. ⁶√5

  4. All are equal

Answer: B

Solution

Approximate values are ∛2≈1.260, √3≈1.732 and ⁶√5≈1.308. Therefore, √3 is the largest.

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Question 73

What is the equation of the line with slope -2 passing through the point (1,-3)?

  1. y=2x+1

  2. y=-x-6

  3. y=-3x+6

  4. y=-2x-1

Answer: D

Solution

Using the point-slope form, y-y₁=m(x-x₁). Thus y+3=-2(x-1), which simplifies to y=-2x-1.

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Question 74

Triangle PQR is similar to triangle XYZ. The ratio of their perimeters is 3:4. What is the ratio of the length of the median from vertex P to the length of the median from vertex X?

  1. 3:4

  2. 9:16

  3. 27:64

  4. 19:17

Answer: A

Solution

For similar triangles, the ratio of corresponding linear measurements, including medians, equals the ratio of corresponding sides and perimeters. Therefore, the ratio is 3:4.

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Question 75

In triangle ABC, line DE is parallel to BC and intersects AB at D and AC at E. If AD=5 cm, DB=7 cm and AE=10 cm, find EC.

  1. 9 cm

  2. 13 cm

  3. 14 cm

  4. 17 cm

Answer: C

Solution

By the Basic Proportionality Theorem, AD/DB=AE/EC. Thus 5/7=10/EC, giving EC=14 cm.

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