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Ratio of incomes and expenditures with equal savings

Write incomes as ax, bx and expenditures as cy, dy. Equal savings give one equation in x and y; solve, then answer what is asked.

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Worked examples

Example 1 · level 1

The monthly incomes of Ayaan and Vihaan are in the ratio 4 : 3, and their expenses are in the ratio 7 : 5. If each saves ₹250 a month, what is Ayaan’s monthly income?

  1. ₹1,000
  2. ₹1,500
  3. ₹1,750
  4. ₹2,000
Show solution
  1. 4x − 7y = 3x − 5y ⇒ 1x = 2y ⇒ y = 1x/2.
  2. Substitute in 4x − 7y = 250 to get x = 500.
  3. Ayaan’s income = 4 × 500 = ₹2,000.

Answer: ₹2,000

Example 2 · level 2

The monthly incomes of Diya and Kabir are in the ratio 4 : 3, and their expenses are in the ratio 9 : 5. If each saves ₹1,750 a month, what is Diya’s monthly income?

  1. ₹2,250
  2. ₹3,000
  3. ₹4,000
  4. ₹7,000
Show solution
  1. 4x − 9y = 3x − 5y ⇒ 1x = 4y ⇒ y = 1x/4.
  2. Substitute in 4x − 9y = 1,750 to get x = 1,000.
  3. Diya’s income = 4 × 1,000 = ₹4,000.

Answer: ₹4,000

Example 3 · level 3

The monthly incomes of Joseph and Lakshmi are in the ratio 7 : 6, and their expenses are in the ratio 5 : 4. If each saves ₹2,000 a month, what is Lakshmi’s monthly income?

  1. ₹4,000
  2. ₹6,000
  3. ₹7,000
  4. ₹12,000
Show solution
  1. 7x − 5y = 6x − 4y ⇒ 1x = 1y ⇒ y = x.
  2. Substitute in 7x − 5y = 2,000 to get x = 1,000.
  3. Lakshmi’s income = 6 × 1,000 = ₹6,000.

Answer: ₹6,000

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