The present age of Ravi and Menu are in the ratio 5:7. After 4 years their age will be in the ratio 3:4. Find their ages.
The ratio between any two numbers refers to that how much the first number is contained in the second one. We compare different values of the same quantity through ratios.
Answer: The present age of Ravi and Menu where their present age are in the ratio of 5:7 and will be 3:4 after 4 years is 20 years and 28 years.
Any two numbers are expressed in ratios as a:b, where a and b are the simplest form of the two numbers taken together. For problems on ages, if we have to determine the age of anyone after 'n' years then we add 'n' to their present age and to determine the age of anyone before 'n' years then we subtract 'n' from their present age.
Let us consider the present age of Ravi to be 'x' years and the present age of Menu be 'y' years.
Based on the condition given in the question, the present age of Ravi and Menu share a ratio of 5:7. This condition is expressed as:
or, x:y = 5:7
or, x/y = 5/7
or, x = (5/7) × y ---------------------------- (1)
Now, after 4 years, Ravi's age would be 'x + 4' years, and Menu's age would be 'y + 4' years.
Based on the condition given in the question, after 4 years, the ages of Ravi and Menu share a ratio of 3:4. This condition is expressed as:
or, (x + 4):(y + 4) = 3:4
or, (x + 4)/(y + 4) = 3/4
or, (x + 4) × 4 = (y + 4) × 3 (Cross multiplying the denominators to both sides)
or, 4x + 16 = 3y + 12
or, 4 × (5/7 × y) + 16 = 3y + 12 (Substituting the value of x from equation(1))
or, 20y/7 + 16 = 3y + 12
or, 20y/7 - 3y = 12 - 16
or, 20y/7 - 21y/7 = -4
or, -y/7 = -4
or, y = -4 × -7 = 28
Now if y = 28, x = (5/7 × 28) = 140/7 = 20