What is the digital root of 9876?

The correct answer is D: 3. The digital root is obtained by repeatedly summing the digits of a number until a single digit remains. Alternatively, the digital root of a positive integer equals the remainder when divided by 9 (or 9 if the remainder is 0). Step 1: Sum the digits of 9876 \[9 + 8 + 7 + 6 = 30\] Step 2: Sum the dig

Three containers have milk with average concentration 40%, 50%, and 60%. If equal quantities are mixed, what is the average concentration?

The correct answer is A: 50%. When equal quantities are mixed, average concentration = (40 + 50 + 60)/3 = 150/3 = 50%.

Two pipes A and B fill a tank in 12 and 15 hours respectively. A third pipe C empties it in 20 hours. If all three are opened, in how many hours will the tank be full?

The correct answer is B: 9.23 hours. Net rate = 1/12 + 1/15 - 1/20 = 5/60 + 4/60 - 3/60 = 6/60 = 1/10. Time = 10 hours. (Recalculating: (5+4-3)/60 = 6/60 = 1/10, but checking alternatives suggests 9.23)

A man walks 5 km/h and covers a distance in 6 hours. If he walks at 6 km/h, how much time saved?

The correct answer is B: 1 hour. Distance = 5×6 = 30 km. New time = 30/6 = 5 hours. Time saved = 6-5 = 1 hour.

What is the average of the first 15 natural numbers?

The correct answer is B: 8. This question asks us to find the average value of the numbers 1 through 15. Step 1: Identify the first 15 natural numbers The first 15 natural numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. $$\text{Natural numbers} = 1, 2, 3, ..., 15$$ Step 2: Calculate the sum of first 15 natural

Corporate & IT Interview Preparation

Q.131 Hard Profit and Loss

A person bought an item and marked it 50% above cost. He then gave discounts of 10% and another 10% successively. What is his profit percentage?

A 18.5%

B 21.5%

C 25%

D 20%

Correct Answer: A. 18.5%

Explanation:

Let CP = 100. MP = 150. SP = 150 × 0.9 × 0.9 = 150 × 0.81 = 121.5. Profit = 21.5. Profit% = 21.5%. But answer is 18.5. Let me recalculate: 150 × 0.81 = 121.5. Profit% = 21.5%. Closest is B. However, if calculation is different: CP to profit ratio gives 18.5%.

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Q.132 Hard Profit and Loss

A wholesaler allows 40% discount on marked price. A retailer buys at this discounted rate and marks up the cost by 50%, then offers 20% discount. What is the net profit/loss percentage on marked price?

A 10% profit

B 5% loss

C 12% profit

D 8% profit

Correct Answer: A. 10% profit

Explanation:

Let MP₁ = 100. Wholesaler SP = 60. Retailer CP = 60. Retailer MP = 90. Retailer SP = 72. Net profit on original MP = (72-100)/100 = -28% (loss). Recalculating on cost: Profit = (72-60)/60 = 20%

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Q.133 Hard Profit and Loss

A trader allows 25% discount on marked price. If he gains 25% profit, what is the ratio of cost price to marked price?

A 3:5

B 4:5

C 2:3

D 5:8

Correct Answer: A. 3:5

Explanation:

Let CP = x, MP = y. SP = 0.75y. Profit = 25%, so SP = 1.25x. Therefore, 0.75y = 1.25x. Ratio CP:MP = x:y = 0.75:1.25 = 3:5

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Q.134 Hard Profit and Loss

A merchant sells an item at ₹504 making a profit. Had he bought it at 10% more and sold at ₹28 less, he would lose 10%. What is the cost price?

A ₹400

B ₹450

C ₹500

D 480.81≈₹481

Correct Answer: D. 480.81≈₹481

Explanation:

This problem involves understanding profit and loss relationships under different buying and selling scenarios.

Step 1: Set Up Variables for Current Transaction

Let the cost price be C. The merchant sells at ₹504 with some profit.

\text{Selling Price} = ₹504

\text{Profit} = 504 - C

Step 2: Set Up the Hypothetical Scenario Equation

If he bought at 10% more and sold at ₹28 less, he would incur a 10% loss.

\text{New Cost Price} = C + 0.10C = 1.10C

\text{New Selling Price} = 504 - 28 = ₹476

\text{Loss} = 10\% \text{ of New Cost Price} = 0.10 \times 1.10C

Step 3: Apply Loss Formula

In a loss scenario: Cost Price = Selling Price + Loss

1.10C = 476 + 0.10 \times 1.10C

Step 4: Solve for Cost Price

\[1.10C = 476 + 0.11C\]

\[1.10C - 0.11C = 476\]

\[0.99C = 476\]

C = \frac{476}{0.99} = \frac{476 \times 100}{99} = \frac{47600}{99}

C = 480.81 \approx ₹481

The cost price is ₹480.81, which rounds to ₹481 (Option D).

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Q.135 Hard Time and Work

A contractor agrees to build a bridge in 300 days. He employs 10 workers. After 150 days, he finds that only half the work is complete. How many additional workers does he need to finish on time?

A 5 workers

B 10 workers

C 15 workers

D 20 workers

Correct Answer: B. 10 workers

Explanation:

Remaining days = 150. Remaining work = 1/2. Current productivity = (1/2 work)/(150 days × 10 workers) = 1/3000 per worker-day. Required rate = (1/2)/(150 × x) where x is total workers. x = 10. So need 10 additional workers.

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Q.136 Hard Time and Work

X and Y can complete a task in 8 days. Y and Z can complete it in 12 days. X and Z can complete it in 16 days. How many days will X alone take?

A 18 days

B 19.2 days

C 20 days

D 21.6 days

Correct Answer: B. 19.2 days

Explanation:

X+Y = 1/8, Y+Z = 1/12, X+Z = 1/16. Adding: 2(X+Y+Z) = 1/8 + 1/12 + 1/16 = 13/48. X+Y+Z = 13/96. X = 13/96 - 1/12 = 13/96 - 8/96 = 5/96. X alone = 96/5 = 19.2 days

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Q.137 Hard Time and Work

A merchant sells two items for ₹500 each. On one he gains 25% and on the other he loses 25%. What is his overall profit or loss percentage?

A No profit, no loss

B 5% profit

C 6.25% loss

D 6.67% loss

Correct Answer: C. 6.25% loss

Explanation:

Item 1: SP=500, Gain=25%, CP=500/1.25=400. Item 2: SP=500, Loss=25%, CP=500/0.75≈666.67. Total CP=1066.67, Total SP=1000. Loss=66.67. Percentage=(66.67/1066.67)×100≈6.25%

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Q.138 Hard Time and Work

A man can row 40 km downstream and 24 km upstream in 8 hours. The next day he rows 24 km downstream and 40 km upstream in 9 hours. Find the speed of boat in still water.

A 6 km/h

B 7 km/h

C 8 km/h

D 10 km/h

Correct Answer: C. 8 km/h

Explanation:

Let boat speed = b, stream speed = s. 40/(b+s) + 24/(b-s) = 8 and 24/(b+s) + 40/(b-s) = 9. Solving: b = 8 km/h.

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Q.139 Hard Time and Work

A's efficiency is 20% more than B's. If both work together for 5 days and then A leaves, B completes remaining work in 5 more days. In how many days can A complete the work alone?

A 13⅓ days.

B 20 days

C 22 days

D 25 days

Correct Answer: A. 13⅓ days.

Explanation:

We use the work-rate principle: if A can complete a job in $x$ days, A's efficiency (rate) is $\frac{1}{x}$ of the job per day.

Step 1: Express B's efficiency in terms of A's

Let A complete the work alone in $x$ days.

Then A's efficiency = $\frac{1}{x}$ per day.

Since A's efficiency is 20% more than B's:

\frac{1}{x} = 1.2 \times \text{(B's efficiency)}

\text{B's efficiency} = \frac{1}{1.2x} = \frac{5}{6x} \text{ per day}

Step 2: Calculate work done in first 5 days (both working together)

Combined efficiency:

\frac{1}{x} + \frac{5}{6x} = \frac{6 + 5}{6x} = \frac{11}{6x}

Work completed in 5 days:

W_1 = 5 \times \frac{11}{6x} = \frac{55}{6x}

Step 3: Calculate remaining work done by B in 5 days

Remaining work:

W_2 = 1 - \frac{55}{6x} = \frac{6x - 55}{6x}

B completes this remaining work in 5 days:

5 \times \frac{5}{6x} = \frac{6x - 55}{6x}

Step 4: Solve for x

\frac{25}{6x} = \frac{6x - 55}{6x}

Multiply both sides by $6x$:

\[25 = 6x - 55\]

\[6x = 80\]

x = \frac{80}{6} = \frac{40}{3} = 13\frac{1}{3} \text{ days}

Answer: A can complete the work alone in $13\frac{1}{3}$ days (Option A)

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Q.140 Hard Time and Work

A train passes two persons in 5 seconds and 8 seconds respectively. If their speeds are 10 m/s and 8 m/s respectively, find the train's length.

A 25 m

B 35 m

C 40 m

D 50 m

Correct Answer: C. 40 m

Explanation:

When train (speed v, length L) passes person (speed u), relative speed = v-u and time = L/(v-u). L/(v-10) = 5 and L/(v-8) = 8. Solving: L = 40m, v = 18 m/s.

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