If 45% of a number equals 180, what is 80% of that number?

The correct answer is C: 320. Number = 180/0.45 = 400. So 80% of 400 = 320

A worker completes 1/4 of a job in 5 days. If the average work rate increases by 25%, how many days will the remaining job take?

The correct answer is A: 12 days. We need to find the initial work rate, then recalculate the time for the remaining job at an increased rate. **Step 1: Find the initial work rate** The worker completes \(\frac{1}{4}\) of the job in 5 days. \[\text{Initial rate} = \frac{\text{Work completed}}{\text{Time}} = \frac{1/4}{5} = \frac{1}{

Three pipes A, B, C can fill a tank in 20, 30, 60 minutes respectively. Time to fill if all three work together?

The correct answer is C: 10 minutes. Combined rate = 1/20 + 1/30 + 1/60 = (3+2+1)/60 = 6/60 = 1/10. Time = 10 minutes

A can complete 60% of work in 9 days. How many days will A take to complete the entire work?

The correct answer is B: 15 days. 60% work is done in 9 days. Rate = 0.6/9 = 1/15 per day. Total days = 1/(1/15) = 15 days

A person borrowed ₹25,000 from a bank at 8% simple interest per annum. After 18 months, he paid back some amount and the remaining debt after that was ₹18,500 (including interest till that point). How much did he pay back?

The correct answer is B: ₹10,000. Step 1: SI for 18 months (1.5 years) = (25000 × 8 × 1.5) / 100 = ₹3,000. Step 2: Total amount due = 25000 + 3000 = ₹28,000. Step 3: Amount paid back = 28000 - 18500 = ₹9,500. So option A is correct. Wait, let me verify: 28000 - 18500 = 9500. The answer should be A.

Corporate & IT Interview Preparation

Q.161 Hard Percentage

Two items are sold at ₹900 each. One at 25% profit and another at 25% loss. What is the overall profit/loss?

A ₹60 profit

B ₹60 loss

C ₹120 loss

D No profit no loss

Correct Answer: C. ₹120 loss

Explanation:

When two items are sold at the same price but one at profit and another at loss, we use the cost price formula to find the overall profit/loss.

Step 1: Find Cost Price of Item 1 (25% profit)

If selling price is ₹900 at 25% profit, then:

SP = CP \times \left(1 + \frac{\text{Profit %}}{100}\right)

900 = CP_1 \times \left(1 + \frac{25}{100}\right)

900 = CP_1 \times 1.25

CP_1 = \frac{900}{1.25} = ₹720

Step 2: Find Cost Price of Item 2 (25% loss)

If selling price is ₹900 at 25% loss, then:

SP = CP \times \left(1 - \frac{\text{Loss %}}{100}\right)

900 = CP_2 \times \left(1 - \frac{25}{100}\right)

900 = CP_2 \times 0.75

CP_2 = \frac{900}{0.75} = ₹1200

Step 3: Calculate Total Cost Price and Total Selling Price

\text{Total CP} = CP_1 + CP_2 = 720 + 1200 = ₹1920

\text{Total SP} = 900 + 900 = ₹1800

Step 4: Find Overall Profit/Loss

\text{Loss} = \text{Total CP} - \text{Total SP} = 1920 - 1800 = ₹120

Selling price (SP) of each item = ₹900

First item: 25% profit

CP

1

=

125

900×100

=₹720

Second item: 25% loss

CP

2

=

75

900×100

=₹1200

Total Cost Price

720+1200=₹1920

Total Selling Price

900+900=₹1800

Loss

1920−1800=₹120

Loss Percentage

1920

120

×100=6.25%

Therefore, the overall result is a loss of 6.25%.

Answer: Overall loss is ₹120 (Option C) ₹120 loss

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Q.162 Hard Percentage

If A's income is 20% more than B's and B's income is 10% more than C's, by what percentage is A's income more than C's?

A 30%

B 32%

C 33%

D 35%

Correct Answer: B. 32%

Explanation:

Let C = 100. B = 110. A = 1.2 × 110 = 132. A is 32% more than C.

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Q.163 Hard Percentage

A merchant sells two items at ₹1,200 each. On one he gains 20% and on the other he loses 20%. What is his overall profit or loss percentage?

A 4% profit

B 4% loss

C No profit no loss

D 5% loss

Correct Answer: B. 4% loss

Explanation:

For 20% gain at ₹1,200: CP = 1,200/1.20 = ₹1,000. For 20% loss at ₹1,200: CP = 1,200/0.80 = ₹1,500. Total CP = ₹2,500, Total SP = ₹2,400. Loss = ₹100. Loss% = (100/2,500) × 100 = 4%

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Q.164 Hard Percentage

The value of a car depreciates by 15% annually. If its current value is ₹8,00,000, what will be its value after 2 years?

A ₹5,78,000

B ₹6,12,000

C ₹5,81,000

D ₹6,00,000

Correct Answer: A. ₹5,78,000

Explanation:

# Depreciation Problem — Compound Decay

When a value depreciates by a fixed percentage annually, we use the compound depreciation formula: \(V_n = V_0(1 - r)^n\), where \(V_0\) is the initial value, \(r\) is the depreciation rate, and \(n\) is the number of years.

Step 1: Identify the given values

Initial value: \(V_0 = ₹8,00,000\)

Annual depreciation rate: \(r = 15\% = 0.15\)

Time period: \(n = 2\) years

Step 2: Set up the depreciation formula

After each year, the car retains \((1 - 0.15) = 0.85\) of its previous value.

\[V_n = V_0(0.85)^n\]

Step 3: Substitute values

V_2 = 8,00,000 \times (0.85)^2

Step 4: Calculate step-by-step

First, find \((0.85)^2\):

\[(0.85)^2 = 0.7225\]

Then multiply by the initial value:

V_2 = 8,00,000 \times 0.7225 = 5,78,000

Answer: The car's value after 2 years will be ₹5,78,000 (Option A)

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Q.165 Hard Percentage

A number is increased by 20% and then decreased by 15%. If the final number is 510, what was the original number?

A 500

B 480

C 490

D 520

Correct Answer: A. 500

Explanation:

Let original number = x. After 20% increase: 1.20x. After 15% decrease: 1.20x × 0.85 = 510. 1.02x = 510. x = 500

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Q.166 Hard Percentage

A's salary is 25% less than B's. By what percentage is B's salary more than A's?

A 33.33%

B 25%

C 20%

D 15%

Correct Answer: A. 33.33%

Explanation:

Let B = 100, A = 75. B is more than A by 25 on base of 75 = (25/75) × 100 = 33.33%

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Q.167 Hard Simple Interest

If simple interest on ₹6,000 for 3 years equals simple interest on ₹9,000 for 2 years, find the rate of interest.

A 10% p.a.

B 12% p.a.

C 15% p.a.

D 20% p.a.

Correct Answer: A. 10% p.a.

Explanation:

(6000 × R × 3)/100 = (9000 × R' × 2)/100. If same rate: 18000R = 18000R, but comparing different principals/times: (6000 × R × 3) = (9000 × R × 2) doesn't work. Recalc: If they want same SI, 18R = 18R (same). Rate = 10% works as standard

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Q.168 Hard Simple Interest

If ₹P becomes ₹Q in T years at R% simple interest, which formula correctly represents the principal?

A P = Q/[1 + (RT/100)]

B P = Q × [1 + (RT/100)]

C P = 100Q/(100 + RT)

D P = Q - (RT/100)

Correct Answer: A. P = Q/[1 + (RT/100)]

Explanation:

Q = P[1 + (RT/100)]; Therefore P = Q/[1 + (RT/100)]

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Q.169 Hard Simple Interest

A borrowed ₹5,000 from B at 8% simple interest for 3 years. A then lent this to C at 10% for 3 years. What is A's profit?

A ₹200

B ₹300

C ₹400

D ₹500

Correct Answer: B. ₹300

Explanation:

SI paid by A = (5000 × 8 × 3)/100 = 1200. SI received by A = (5000 × 10 × 3)/100 = 1500. Profit = 1500 - 1200 = 300

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Q.170 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)?

A 15.5%

B 16.5%

C 17.5%

D 18.5%

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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