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Aptitude · Lesson 3 of 9

Ratio, proportion & partnership

Simplifying and combining ratios, dividing amounts and sharing profit.

  • A ratio a : b compares quantities; simplify by dividing both by their HCF.
  • To divide an amount S in ratio a : b, the parts are S × a/(a+b) and S × b/(a+b).
  • Combine A:B and B:C by making B equal in both (multiply to a common value).
  • Proportion: a : b = c : d means a × d = b × c.
  • Partnership: profit is shared in the ratio of capital × time for each partner.

Example: A : B = 2 : 3 and B : C = 4 : 5. Find A : B : C.

  1. Make B equal: 2 : 3 becomes 8 : 12 (×4) and 4 : 5 becomes 12 : 15 (×3).
  2. Combine with B = 12.

Answer: 8 : 12 : 15

Example: Asha invests ₹60,000 for 12 months and Binu invests ₹90,000 for 8 months. Out of a profit of ₹50,000, what is Asha's share?

  1. Asha: 60,000 × 12 = 7,20,000. Binu: 90,000 × 8 = 7,20,000.
  2. Ratio = 1 : 1.

Answer: ₹25,000

Key points

  • Divide S in a:b → S×a/(a+b).
  • Match the common term to combine ratios.
  • Partnership share ∝ capital × time.

Quick check

Divide ₹900 in the ratio 4 : 5. The larger share is…

Practice task

₹7,200 is divided among P, Q and R in the ratio 3 : 4 : 5. How much does R get?

Show answer

Total parts = 12; R = 7,200 × 5/12 = ₹3,000.

Interview corner

The ratio of boys to girls is 3:2 with 40 girls. How many students?

One part = 40/2 = 20; total = 5 parts = 100.

What is the fourth proportional to 4, 9 and 12?

4 : 9 = 12 : x → x = 9 × 12 / 4 = 27.

Original lesson written by the InfoparkDaily team · © 2026 InfoparkDaily · Free to learn — no paid course or subscription.