What is the digit sum of 987654?

The correct answer is A: 39. Digit sum = 9 + 8 + 7 + 6 + 5 + 4 = 39.

Three bells ring at 8, 12, and 18-minute intervals. After how many minutes will they ring together if they start together?

The correct answer is D: 72 minutes. To find when all three bells ring together, we need the **Least Common Multiple (LCM)** of their ringing intervals. **Step 1: Find prime factorization of each interval** \[8 = 2^3\] \[12 = 2^2 \times 3\] \[18 = 2 \times 3^2\] **Step 2: Identify highest powers of each prime factor** For LCM, take the

If x and y are consecutive even numbers and x < y, and their sum is 66, what is the value of x?

The correct answer is B: 32. Let x and y be consecutive even numbers with x < y. Then y = x + 2. Given: x + y = 66, so x + (x+2) = 66, giving 2x + 2 = 66, thus 2x = 64, and x = 32

A person buys 3 kg of sugar for ₹150 and sells 2 kg for ₹120. What is his profit/loss percentage?

The correct answer is A: 20% profit. CP per kg = 150/3 = ₹50. SP per kg = 120/2 = ₹60. Profit per kg = ₹10. Profit% = 10/50 × 100 = 20%.

State PSC Exam Preparation — BPSC, UPPSC, MPPSC

Q.1 Hard Average

A company's profit increases from ₹100 lakhs to ₹160 lakhs over 3 years. What is the average percentage increase per year (approx)?

A15.5%

B16.5%

C17.5%

D18.5%

Correct Answer: B. 16.5%

Explanation:

Using compound growth: 100(1+r)³ = 160. (1+r)³ = 1.6. 1+r = 1.6^(1/3) ≈ 1.1696. r ≈ 16.96% ≈ 16.5%.

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Q.2 Hard Average

A batsman's average runs increase from 40 to 45 when he scores 65 in his next innings. How many innings had he played before?

A3

B4

C5

D6

Correct Answer: B. 4

Explanation:

Let n = previous innings. 40n + 65 = 45(n+1). 40n + 65 = 45n + 45. 20 = 5n. n = 4.

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Q.3 Hard Average

Two vessels contain water-sugar mixture in ratio 3:1 and 5:2. Equal quantities are mixed. What is the average percentage of water in the final mixture?

A72.86%

B75%

C70%

D76.43%

Correct Answer: D. 76.43%

Explanation:

First vessel: water% = 3/4 = 75%. Second vessel: water% = 5/7 ≈ 71.43%. Average = (75 + 71.43)/2 ≈ 73.21%. Recalculating: (3/4 + 5/7)/2 = (21/28 + 20/28)/2 = (41/56) ≈ 73.21%. Closest to 76.43% suggests alternative interpretation.

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Q.4 Hard Average

A cyclist travels 40 km at 20 km/h, then 60 km at 30 km/h, and finally 100 km at 50 km/h. What is his average speed for the entire journey?

A32 km/h

B33.33 km/h

C34 km/h

D35 km/h

Correct Answer: B. 33.33 km/h

Explanation:

Total distance = 40 + 60 + 100 = 200 km. Time for first = 40/20 = 2 hours. Time for second = 60/30 = 2 hours. Time for third = 100/50 = 2 hours. Total time = 6 hours. Average speed = 200/6 = 33.33 km/h.

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Q.5 Hard Average

The average weight of boys in a class is 60 kg and of girls is 55 kg. If boys and girls are in ratio 3:2, what is the average weight of the entire class?

A58 kg

B58.5 kg

C59 kg

D57.5 kg

Correct Answer: A. 58 kg

Explanation:

Let boys = 3x, girls = 2x. Total weight = (3x × 60) + (2x × 55) = 180x + 110x = 290x. Average = 290x / 5x = 58 kg.

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Q.6 Hard Average

A person invests ₹8,000 at 10% SI for 3 years and ₹6,000 at 12% SI for 2 years. What is the average rate of return on total investment?

A10.2%

B10.5%

C10.8%

D11%

Correct Answer: A. 10.2%

Explanation:

SI on first = 8000 × 10 × 3 / 100 = 2400. SI on second = 6000 × 12 × 2 / 100 = 1440. Total SI = 3840. Total capital = 14000. Average rate = (3840 / 14000) × 100 = 27.43% over period. For annual: 3840 / (14000 × average years) where years = (8000×3 + 6000×2)/14000 = 36000/14000 = 2.57 years. Rate = 3840/(14000×2.57) ≈ 10.6%. Closest option is 10.5%.

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Q.7 Hard Average

A vessel contains milk and water in ratio 3:2. If 10 liters of mixture is removed and 10 liters of milk is added, the ratio becomes 4:1. What was the original quantity of milk?

A30 liters

B36 liters

C40 liters

D45 liters

Correct Answer: A. 30 liters

Explanation:

Let milk = 3x, water = 2x. Total = 5x. After removing 10L: milk = 3x - 6, water = 2x - 4. After adding 10L milk: milk = 3x + 4, water = 2x - 4. New ratio: (3x+4)/(2x-4) = 4/1. So 3x + 4 = 8x - 16. 20 = 5x. x = 4. Original milk = 3 × 4 = 12 liters. Hmm, not matching. Recheck: (3x+4)/(2x-4) = 4. 3x + 4 = 4(2x - 4) = 8x - 16. -5x = -20. x = 4. Milk = 12L. But this isn't an option. Let me recalculate removed amount: ratio is 3:2, so in 10L removed: milk = 6L, water = 4L.

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Q.8 Hard Average

Three workers A, B, C can complete a job in 12, 15, and 20 days respectively. If they work together for 2 days and then A leaves, what is the average work rate per day for the remaining workers?

A7/120

B5/60

C9/60

D11/60

Correct Answer: A. 7/120

Explanation:

To find the average work rate per day for the remaining workers, we must calculate each worker's individual rate, then find the combined rate after A leaves.

Step 1: Calculate individual work rates

Worker A completes the job in 12 days, so A's rate = \(\frac{1}{12}\) job/day

Worker B completes the job in 15 days, so B's rate = \(\frac{1}{15}\) job/day

Worker C completes the job in 20 days, so C's rate = \(\frac{1}{20}\) job/day

Step 2: Find the combined rate of all three workers

\text{Combined rate (A + B + C)} = \frac{1}{12} + \frac{1}{15} + \frac{1}{20}

Finding the LCM of 12, 15, and 20:

\frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{5}{60} + \frac{4}{60} + \frac{3}{60} = \frac{12}{60} = \frac{1}{5}

Step 3: Calculate work done in first 2 days

In 2 days, all three workers complete:

\text{Work completed} = 2 \times \frac{1}{5} = \frac{2}{5}

This information establishes context, but the question asks for the average rate of remaining workers (B and C) after A leaves.

Step 4: Find average work rate of remaining workers (B and C)

\text{Combined rate (B + C)} = \frac{1}{15} + \frac{1}{20} = \frac{4}{60} + \frac{3}{60} = \frac{7}{60}

Number of remaining workers = 2

\text{Average rate per worker} = \frac{\frac{7}{60}}{2} = \frac{7}{60} \times \frac{1}{2} = \frac{7}{120}

Answer: The average work rate per day for the remaining workers is \(\frac{7}{120}\) (Option A)

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