1.Two numbers are in the ratio 5 to 9. If 5 is subtracted from each number, the new ratio becomes 5 to 11. What are the original numbers?
2.What is the third proportional to the numbers 3.5 and 5.6?
3.A cookie recipe requires combining 400 grams of flour with 500 grams of sugar. If you only have 300 grams of flour available, how much sugar should you use to keep the same ratio?
4.Given three quantities X, Y, and Z of the same type where the ratio of X to Y is 5 to 8, and the ratio of Y to Z is 4 to 7, what is the ratio of X to Z?
5.Two varieties of rice are priced at Rs.13 per kg and Rs.19 per kg respectively. In what ratio should these two types be combined so that the resulting mixture costs Rs.14.2 per kg?
6.Four individuals A, B, C, and D share a sum of money in the ratio 7:4:3:2 respectively. If D's share is Rs. 500 less than A's share, what is the total amount of money?
7.If x is 20% greater than z and y is 80% greater than z, what is the ratio of x to y?
8.Find the value of x that satisfies the proportion: (2x) : 25 = 6 : (x/3).
9.Which of the following ratios cannot represent two natural numbers whose sum is 72?
10.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)?
11.If p is 50% greater than q, what is the ratio of p to q?
12.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?
13.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?
14.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?
15.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?
16.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?
17.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.
18.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?
19.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?
20.Determine the fourth proportional number corresponding to 3, 7, and 9.