Govt. Exams
Entrance Exams
P(1.2)² = 14400. P × 1.44 = 14400. P = Rs. 10000
Downstream speed = 72/3 = 24 km/h. Upstream speed = 72/6 = 12 km/h. Current = (24-12)/2 = 6 km/h
Net rate = 1/20 + 1/30 - 1/40 = 6/120 + 4/120 - 3/120 = 7/120. Time = 120/7 ≈ 17.14 minutes
# Solution: Profit Calculation with Markup and Discount
Understanding profit requires calculating the selling price after applying markup and discount to the cost price.
Step 1: Calculate the Marked Price
The merchant marks goods 50% above the cost price of Rs. 8000.
Step 2: Calculate the Selling Price After Discount
A discount of 10% is given on the marked price of Rs. 12000.
Step 3: Calculate the Profit
Profit is the difference between selling price and cost price.
The merchant's profit is Rs. 2800.
Answer: (D) Rs. 2800 ✓
Net rate = 1/10 + 1/15 - 1/20 = 6/60 + 4/60 - 3/60 = 7/60. Time = 60/7 ≈ 8.57 hours.
Rate = (10125/9000 - 1) × 100 = (1.125 - 1) × 100 = 12.5%.
CP per banana = 5/6. SP per banana = 6/5. Profit % = ((6/5 - 5/6)/(5/6)) × 100 = ((36-25)/30)/(5/6) × 100 = (11/30) × (6/5) × 100 = 44%.
Work rate problems require finding individual rates and combining them to determine completion time.
Step 1: Find Individual Work Rates
Each person's work rate is the fraction of work completed per day (reciprocal of days needed).
Step 2: Find Combined Work Rate
When working together, their rates add up. Find the LCM of 6, 8, and 12, which is 24.
Step 3: Calculate Time to Complete Half Work
Using the formula: Time = Work ÷ Rate
The answer is (A) 1.5 days.
14641/10000 = 1.4641. (1+r)^4 = 1.4641. 1+r = 1.11. r = 11%.
When two trains cross each other, the total distance covered equals the sum of their lengths, and we use the relative speed to find this distance.
Step 1: Convert speed to m/s
The moving train travels at \(80\text{ km/h}\). Convert to metres per second:
Step 2: Find distance covered in 18 seconds
Distance = Speed × Time
Step 3: Apply the crossing condition
When the moving train completely crosses the stationary train, the distance covered equals the sum of both train lengths:
where \(L_{\text{moving}}\) is the length we need to find and \(L_{\text{stationary}} = 200\text{ m}\).
Step 4: Calculate the length of the moving train
Answer: The length of the moving train is \(200\text{ m}\) (Option A)
