UPSC Prelims 2026 · CSAT (Paper II): The speed of a train T is 100 km per hour and the speed…
The speed of a train T is 100 km per hour and the speed of a person P is 4 km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T. If P travels along the opposite direction of T, then in how much time does T cross P, in seconds, approximately?
Answer (c) & explanation
The train crosses him in about 13.85 seconds (c). Step 1: same direction: relative speed = 100 − 4 = 96 km/h. The train takes 15 seconds to pass him. Step 2: opposite direction: relative speed = 100 + 4 = 104 km/h. The train's length stays the same, so time falls in proportion. Step 3: time = 15 × 96 ÷ 104 = 1440 ÷ 104 ≈ 13.85 seconds. Options (a), (b) and (d) are close numbers from rounding or arithmetic slips.
Tip: when the distance (train length) is the same, time is inversely proportional to relative speed. No need to find the length itself.
Answer as per the official UPSC answer key.
Related questions from other years
Read the passage
How is deflation done? Most countries use a method called ‘double deflation’, where input and output prices are deflated separately. Consider a manufacturer importing oil for use in production. If oil prices fall, output prices do not and quantities remain the same, real value added should not change. But if the same deflator is used for inputs and outputs, as in India, it would look as if the manufacturer had become more productive.
Which of the following statements is/are correct?
- 1. Real value should not change in the instance of static output cost and unchanged quantities against falling oil prices.
- 2. Deflators are to be used separately for inputs and outputs, and this is a practice universally adopted by all economies.
Select the answer using the code given below.
Answer (d) & explanation
Neither statement is correct (d). Step 1: the passage says if oil prices fall while output prices and quantities stay the same, real value added should not change. Statement 1 changes this to "real value" and "static output cost", which distorts the idea. So 1 is not correct as worded. Step 2: statement 2 says separate deflators are used "universally" by all economies. But the passage says India uses the same deflator for both. So 2 is false. Step 3: options (a), (b) and (c) fail.
Tip: in economic passages, exact terms matter: "value added" is not "value", and "price" is not "cost". "Universally" is disproved by a single exception, here India.
Answer as per the official UPSC answer key.
P, Q, R, S and T are ranked 1 to 5 (not necessarily in that order). The rank of P is 4, the rank of Q is not 5, the rank of R is 1, the rank of S is not 2, the rank of T is not 3. Then which of the following is/are correct?
- I. If the rank of S is 3, then that of T is 2.
- II. If the rank of Q is 3, then that of T is 5.
Select the answer using the code given below.
Answer (d) & explanation
Neither statement is correct (d). Step 1: P = 4 and R = 1 are fixed. Ranks 2, 3 and 5 remain for Q, S and T, with rules: Q is not 5, S is not 2, T is not 3. Step 2: statement I: if S = 3, then Q and T share 2 and 5. Q cannot be 5, so Q = 2 and T = 5, not 2. I is wrong. Step 3: statement II: if Q = 3, then S and T share 2 and 5. S cannot be 2, so S = 5 and T = 2, not 5. II is wrong. Options (a), (b) and (c) fail.
Tip: fix the known ranks first, then apply each "if" condition and let the "not" rules decide the rest. Write the small table on paper.
Answer as per the official UPSC answer key.
How many times does 5 appear in all two-digit positive integers?
Answer (b) & explanation
The digit 5 appears 19 times (b). Step 1: 5 in the tens place: 50, 51, …, 59 = 10 times. Step 2: 5 in the units place: 15, 25, 35, 45, 55, 65, 75, 85, 95 = 9 times (05 is not a two-digit number). Step 3: total = 10 + 9 = 19. The number 55 has two 5s, and both are counted. Option (a), 18, counts 55 once. Options (c) and (d) wrongly add 05 or 5.
Tip: count place by place. The question asks how many times the digit appears, not how many numbers contain it (that would be 18).
Answer as per the official UPSC answer key.
An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio, amounts of P and Q be mixed in order to get R?
Answer (a) & explanation
P and Q must be mixed in the ratio 1 : 3 (a). Step 1: "equal copper and zinc" means R is 50% copper. Step 2: use alligation on copper: P has 20%, Q has 60%, and the mix needs 50%. P : Q = (60 − 50) : (50 − 20) = 10 : 30. Step 3: simplify to 1 : 3. Check: 1 kg P gives 0.2 kg copper; 3 kg Q gives 1.8 kg; total 2 kg copper in 4 kg = 50% ✓. Option (b) reverses the ratio. Options (c) and (d) fail.
Tip: in alligation, the amount of each item is the distance of the other item from the mean. Always check with a quick calculation.
Answer as per the official UPSC answer key.