Let numbers be 3x, 5x. (3x-9)/(5x-9) = 12/23. 69x - 207 = 60x - 108 => 9x = 99 => x = 11. Smaller number = 33.
7253
The salaries of A, B, C are in the ratio 1:3:4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio:
Initial Milk = 40L, Water = 20L. We want 40 / (20 + x) = 1 / 2 => 80 = 20 + x => x = 60 liters.
7255
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Initial syrup fraction = 5/8. We want final syrup fraction = 1/2. Let fraction x be replaced. Syrup left = (5/8)*(1 - x). (5/8)(1 - x) = 1/2 => 1 - x = 4/5 => x = 1/5.
7256
The ratio of A's age to B's age is 4:3. 'A' will be 26 years old after 6 years. The present age of B is:
Let girls be G and boys be B. B + G = 100. 3.6B + 2.4G = 312. Substitute B = 100 - G: 3.6(100 - G) + 2.4G = 312 => 360 - 3.6G + 2.4G = 312 => 1.2G = 48 => G = 40.
7258
The ages of two persons are in the ratio 5:7. 18 years ago their ages were in the ratio of 8:13. Their present ages are:
