UPSC Prelims 2024 · CSAT (Paper II): A certain number of men can complete a piece of work in 6k days,…
A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5k days?
Answer (c) & explanation
The men must increase by 20% (c). Step 1: total work = men × days. So if M men take 6k days, M × 6k = M′ × 5k, where M′ is the new number of men. Step 2: M′ = 6M/5 = 1.2M. Step 3: the increase is 0.2M, that is 20%. Note that k cancels out, so its value does not matter. Option (b), 16.67%, is the fall in days (1k out of 6k), a common mix-up. Options (a) and (d) are wrong.
Tip: men and days are inversely related. If days go from 6 to 5, men go from 5 to 6, an increase of 1 on 5 = 20%. Always take the percentage on the old value.
(b) is the trap: 50/3% is the cut in days for the reverse change, not the rise in men.
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Answer as per the official UPSC answer key.
Related questions from other years
Question : X receives three coins of different denominations : 1, 2, 5, 10 and 20. If the total amount received by X is m, does X receive a coin of denomination 5?
Statement I : m is not a prime number.
Statement II : The sum of the digits of m is greater than 5.
Answer (a) & explanation
Statement II alone is enough; Statement I alone is not (a). Step 1: three different coins from 1, 2, 5, 10, 20 give ten totals. With a 5: 8, 16, 17, 26, 27, 35. Without a 5: 13, 23, 31, 32. Step 2: Statement I (m not prime): 8, 16, 26, 27, 35 have a 5, but 32 (2 + 10 + 20) does not. Mixed answers, so I fails. Step 3: Statement II (digit sum above 5): 8, 16, 17, 26, 27, 35 qualify, and every one has a 5. (13, 23, 31, 32 have digit sums 4, 5, 4, 5.) So II answers "yes". Options (b), (c) and (d) fail.
Tip: when cases are few, list them all. Then check each statement against the full list.
don't assume both statements are needed. Listing all ten cases takes thirty seconds and settles it.
Answer as per the official UPSC answer key.
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 assumptions is/are valid?
- 1. Deflation strategies can be used to make manufacturers appear to be doing better than they actually are.
- 2. When input and output prices are both deflated against a single input price, it is referred to as ‘double deflation’.
Select the answer using the code given below.
Answer (a) & explanation
Only assumption 1 is valid (a). Step 1: the passage says that using one deflator for inputs and outputs, as in India, makes it "look as if the manufacturer had become more productive". So deflation methods can make firms appear better than they are (1). Step 2: assumption 2 says double deflation means deflating both against a single price. But the passage defines double deflation as deflating inputs and outputs separately. So 2 reverses the definition. Step 3: options (b), (c) and (d) fail.
Tip: check definitions word for word against the passage. Deflating means removing the effect of price changes to find real growth, as in real GDP.
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.