First, find the least 2 digit number which gives remainder 4. That number is 11. So, the equation is like 7(x) + 4, where x = 4...13. x cant be greater than 13 as the highest 2 digit number is 95. So, sum = 7(1 + 2 + ... + 13) + 4.13 = 689, using AP series. So, option 3 is correct.

2 ^ {100} = 2 ^ {4} ^ {25} = (4.4) ^ {25} = (15 + 1) ^ {25} = (3.5 + 1) ^ {25} Now, as we divide the expression, (3.5 + 1) ^ {25} by 3, the first part, i.e. 3.5 is divisible by 3. The second part 1 will remain as a remainder, i.e. (1) ^ {25} = 1. So, the remainder is 1. Therefore, option 2 is correct.

Suppose, the total distance is x km. So, one-fourth of the distance is covered in x/100 hours. Rest of the distance is covered in 3x/200 hours. So, avearge speed = total distance/total time = x/(5x/200), i.e. 40. So, the average speed is 40 km/hr. Therefore, option 4 is correct.

Let us assume that the average of all 19 persons is X. So, the total expenditure of 13 members is 13 * 79 and the rest of the people is 6(X + 4). As per the equation: 19X = 13 * 79 + 6(X + 4) => X = 1051/13 = 80.84 (approx). So, option 4 is correct.

As per the given data: X = Z * (80/100) => X is 20% less than Z. Y = Z * (72/100) => Y is 28% less than Z. Lets assume Y is m% less than X. So, Y = X(100 - m)/100 => z * (72/100) = Z * (80/100) (100 -m)/100 => m = 90 =>100 - m = 10 So, Y is 10 % less the number X. Option 5 is correct.

Option 5 is correct.

The pot contains 50 litres of water. As 5 litres of water is taken out and mixed with wine, the ratio of water : wine becomes 5 : 45, i.e. 1 : 9. Again, the same process is repeated. But, this time in 5 litres of solution, wine and water both are replaced in a ratio of 1 : 9. So, the present wine in the pot = (5 - 0.5 + 5) as 5 litre of wine is mixed in the pot again, i.e. wine becomes 9.5 litres. At the same time, the water remains as (45 - 4.5), i.e. 40.5. So, the ratio of wine : water = 9.5 : 40.5 => 19 : 81. So, option 2 is correct.

We know that profit is counted on the cost price and discount is counted on the marked price. Now, the cost of assembling is Rs 400. So, the selling price has to have a 20% profit after 4% discount on the marked price. Then, SP (selling price) after discount = 400 * 120/100 = 480 Now, let us assume the marked price is X and is discounted at 4%. So, X * 96/100 = 480, i.e. X = 500. Option 4 is correct.

Let us assume that money invested is X and it becomes triple @ r % in 8 years. So, interest + principle = 3X, i.e. X * r * 8/100 + X = 3X => r = 25 % Now in 20 years, interest + principle = X(1 + 25 * 20/100) = 6X, i.e. 6 times of the sum invested. So, option 1 is correct.

Option 3 is correct.

Let us assume that the tenure is n years. As the calculation is as per simple interest: Total interest = 900 * 4 * n/100 + 1100 * 5* n/100, i.e. 91n => 91 n = 364 (as per given data) So, n = 4 years, i.e. the tenure is 4 years. So, option 2 is correct.

Let us assume that the price was Rs. X/kg. The price got a hike @ 25% as 125X/100. Now, the person was able to purchase 400/X, but due to the hike it would be 400 * 100/125X. As per the equation, 400/X - 400 * 100/125x = 20, i.e. X = 4 So, the increased price is 4 * 125/100 = 5 Rs/kg Option 1 is correct.

Assume that the sum is X; As per SI /simple interest - interest = 3X/10 = 0.3X As per CI/compound interest - interest = X{ - 1} = 0.331X As per the given data, 0.331X - 0.3X = 620 => X = 20,000

So, option 5 is correct.

Let us assume the cost price = 100 X. Then, selling price = 120 X. Now, the price changes to 1.2 times, so the selling price would be 144X. As per the given data: Profit would be 44X = 40/100 => X = 1000/11 => 120X = 120 * (1000/11) = 10909.09 Option 5 is correct.

Assume X kg from box A and Y kg from box B are to be taken. So, from box A: Rice = 5X/8 and Dal = 3X/8 and from box B : Rice = 7Y/10 and Dal = 3Y/10 So, (5X/8 + 7Y/10) = 6 => 25X + 28Y = 240 (3X/8 + 3Y/10)= 3 => 15X + 12Y = 120 Solving both the equations: X = 4; Y = 5 So, 4 kg from box A and 5 kg from box B are to be taken. So, option 1 is correct.