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CAT 2017 Slot 1 · Quant · Ratio and Partnership · easy

The monthly incomes of Asha and Bela are in the ratio 5 : 2. If each of them saves ₹1,600 per month, what is Asha's monthly income?

Single correct option

The monthly incomes of Asha and Bela are in the ratio 5 : 4 and their monthly expenditures are in the ratio 3 : 2. If each of them saves ₹1,600 per month, what is Asha's monthly income?
  1. A. ₹4,000
  2. B. ₹4,400
  3. C. ₹4,800
  4. D. ₹3,600
Show answer and solution

Answer: (A) ₹4,000

Let incomes be 5x and 4x, and expenditures be 3y and 2y.

Savings: 5x − 3y = 1600 … (i)
4x − 2y = 1600, i.e. 2x − y = 800, so y = 2x − 800 … (ii)

Substitute (ii) in (i): 5x − 6x + 2400 = 1600 → x = 800.

Asha's income = 5x = ₹4,000. (Check: y = 800, expenditures 2400 and 1600; savings 1600 each.)

Tip: Option-checking is fast here: income 4000 → Bela 3200; expenditures 2400 and 1600 are in ratio 3 : 2 ✓.
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