Math Problems and Logic Puzzles

Upstream speed = 45/9 = 5 km/hr. Downstream speed = 49/7 = 7 km/hr. Speed in still water = (Downstream + Upstream) / 2 = (7 + 5) / 2 = 6 km/hr.

After 2 years: Rakesh's plot value = 2.3 × 1.1² = 2.3 × 1.21 = Rs. 2.783 lakh. Ashish's flat value = 2.47 × 1.05² = 2.47 × 1.1025 = Rs. 2.723175 lakh. When they exchange, Rakesh gives property worth Rs. 2.783 lakh and receives property worth Rs. 2.723175 lakh. The difference is 2.783 - 2.723175 = Rs. 0.059825 lakh = Rs. 5982.50. Since Rakesh's property was worth more, Ashish must pay Rakesh the difference.

Let the water:liquid ratio be k:1. For every k units of water (free), we have 1 unit of liquid costing Rs. 18. Total mixture = k + 1 units, so cost per unit = 18/(k + 1). Selling at Rs. 19.2 with 20% profit means cost price should be 19.2/1.2 = Rs. 16. So 18/(k + 1) = 16, giving k + 1 = 18/16 = 9/8, so k = 1/8. Ratio water:liquid = 1:8. Option D is correct.

With 26 players (A-Z) playing each other once, no draws, and distinct scores matching alphabetical order: A > B > C > ... > Z in points. M comes before N alphabetically, so M must have more points than N. Since M and N played each other and there are no draws, one had to win. For M to finish with more points than N, M must have won their head-to-head match. Option C is correct.

10 customers each purchased Rs. 3000, totaling Rs. 30,000. For maximum shopkeeper earnings: If all take 15% discount, shopkeeper gets 30,000 × 0.85 = Rs. 25,500. If all take the 7% discount ticket but redeem it at 4% of purchase value, shopkeeper gets 30,000 × 0.96 = Rs. 28,800. The maximum earnings of Rs. 28,800 occurs when all customers choose to redeem their tickets at 4% rather than taking the immediate 15% discount. Option A is correct.

Let original price = P. Reduced by 33.33% means new price = P × (2/3). With Rs. 99, Atul can buy 99/P kg at original price and 99/(2P/3) = 297/(2P) kg at reduced price. Difference = 297/(2P) - 99/P = 99/(2P) = 3 kg. So 99 = 6P, P = Rs. 16.5. Reduced price = 16.5 × 2/3 = Rs. 11 per kg. Option B is correct.

A number is divisible by 8 if its last three digits are divisible by 8. The sequence ends in ...7374. 374 divided by 8 is 46 with a remainder of 6 (8*46=368; 374-368=6).

Let x be workers and y be bats per worker. xy=320. If (x-n) workers show up, they make (y+24) bats. Testing 8 workers: 320/8=40 bats each. If 3 don't show, 5 workers make 320/5=64 bats. 64-40=24. Thus, 8 were appointed and 3 failed to report.

Let x = number of 20 paise coins and y = number of 50 paise coins. We have: x + y = 50 and 20x + 50y = 1900 paise (converting Rs. 19 to paise). From x + y = 50, x = 50 - y. Substituting: 20(50 - y) + 50y = 1900, giving 1000 - 20y + 50y = 1900, so 30y = 900 and y = 30. Therefore x = 50 - 30 = 20. There are 20 twenty-paise coins. Option E is correct.

A hexagon has 6 sides and a pentagon has 5 sides (a reduction of one). A rectangle has 4 sides; reducing the side count by one results in a triangle (3 sides).

A stick is the primary equipment used to play hockey. A shuttle (or shuttlecock) is the primary object hit in the sport of badminton. Racket is a distractor as it is the tool, not the sport.

Propulsion, fuel, and combustion are all related to the mechanics of engines and movement. Gravity is a fundamental natural force of attraction, making it the odd one out in this context.

Caddies are to golf what ballboys are to tennis - both are support personnel who assist players during matches. In golf, caddies carry clubs, offer advice, and help players navigate the course. Similarly, ballboys in tennis retrieve balls and ensure smooth play. Rowing, bridge, and wrestling do not have equivalent support roles.

Azure is a specific shade of blue. Similarly, auburn is a specific shade of reddish-brown. Therefore, the relationship is a specific color to its general color category.

All 12 months in the Gregorian calendar have at least 28 days. The question asks how many months 'have 28', which applies to the entire year, not just February.