Two numbers are in the ratio 7 : 11. If the first number is increased by 10 and the second number is decreased by 20, then the ratio becomes 2 : 3. What is the sum of the original two numbers?

Explanation

Given: ​ Ratio of two numbers = 7 : 11 First number increased by 10 Second number decreased by 20 New ratio = 2 : 3 Formula Used: If ratio is a : b, numbers are ax and bx Solution: Let the numbers be 7x and 11x 7x + 10 2 = 11x − 20 3 ​ ​ 3(7x + 10) = 2(11x − 20) 21x + 30 = 22x − 40 x = 70 Original numbers = 7x = 490, 11x = 770 Sum = 490 + 770 = 1260 Final Answer: 1260 ​ ​