1.A total distance of 750 km was traveled partly by car (x km) and partly by train (y km). If the train journey exceeded the car journey by 150 km, what is the ratio of the distance traveled by car to that by train (x:y)?
2.If p is 50% greater than q, what is the ratio of p to q?
3.The sum of the squares of three numbers is 280. If these numbers are in the ratio 3:5:6, what is the largest number?
4.A flat is priced at Rs. 4500 per square foot, while a commercial property is priced at Rs. 9500 per square foot. If the total cost of both properties is equal, what is the ratio of their respective areas?
5.Three numbers add up to 172. The ratio between the first and second numbers is 8 to 11, while the ratio between the second and third numbers is 5 to 7. What is the value of the second number?
6.An amount of Rs.130000 is to be shared among 4 singers, 5 dancers, and 3 hosts. It is given that the total sum received by 3 hosts equals that of 2 dancers, and the total sum received by 3 dancers equals that of 2 singers. How much does each singer get?
7.The sum of the cubes of two numbers is 280. If these numbers are in the ratio 2 to 3, what is the smaller number?
8.Determine the value of x when y equals 5, given that x is directly proportional to (4y - 1) and x is 14 when y is 2.
9.The seats allocated for Biology and Computer Science in a school are in the ratio 5 to 8. If the number of seats for Biology is increased by 30% and for Computer Science by 25%, what will be the new ratio of seats?
10.Given the ratios A to B is 2 to 3, B to C is 3 to 4, and A to D is 4 to 5, what is the ratio of C to D?
11.Determine the fourth proportional number corresponding to 3, 7, and 9.
12.If 40% of one number equals two-thirds of a different number, what is the ratio of the first number to the second number?
13.The number of seats allocated for Mathematics, Physics, and Biology in a school are in the ratio 5:7:8. If these seats are increased by 40%, 50%, and 75% respectively, what will be the new ratio of seats?
14.A collection of coins contains 25 paise, 10 paise, and 5 paise coins in the ratio 1 : 2 : 3. If the total amount is Rs. 30, how many 5 paise coins are present?
15.Two numbers have a ratio of 3 to 5. After subtracting 9 from each number, their ratio becomes 12 to 23. What is the value of the smaller number?
16.If two numbers are 20% and 50% greater than a third number respectively, what is the ratio between these two numbers?
17.A certain amount of money is to be divided among A, B, C, and D in the ratio 5 : 2 : 4 : 3. If C receives Rs. 1000 more than D, what is the amount allocated to B?
18.In a college, the ratio of boys to girls is 7 to 8. If the number of boys increases by 20% and the number of girls increases by 10%, what will be the new ratio of boys to girls?
19.The total of three numbers is 98. Given that the ratio of the first number to the second is 2 to 3, and the ratio of the second number to the third is 5 to 8, what is the value of the second number?
20.A two-digit number's digits are swapped to form a new number that is 18 greater than the original. If the sum of the digits is 8, what is the original number?