JEE Advanced Maths: Basic Algebra / Ratio and Proportion questions with solutions

Q1. The sum of two numbers is s and their ratio (quotient) is p/q. Find the two numbers.

1. sp/(p+q) and sq/(p+q)
2. s(p+q)/(p-q) and s(q-p)/(p-q)
3. s/(p+q) and s/(p-q)
4. Cannot be determined

Answer: sp/(p+q) and sq/(p+q)

Since the quotient of the two numbers is p/q, they are in the ratio p: q, so write them as pk and qk. Their sum is pk + qk = (p+q)k = s, giving k = s/(p+q). Therefore the numbers are pk = sp/(p+q) and qk = sq/(p+q).