40% of Ranita’s income is equal to 56% of Bhaskar’s income. If Ranita’s income was ₹800 more than what it is and Bhaskar’s income was ₹ 2,000 more than what it is, then the ratio of the incomes of Ranita and Bhaskar would have been 4 : 3. What is the actual combined income of Ranita and Bhaskar?
Explanation:
Let Ranita's income be R and that of Bhaskar be B.
Given, 40% of R = 56% of B ⇒ 0.4R = 0.56B ⇒ R : B = 0.56 : 0.4 = 56 : 40 = 7 : 5
∴ R = 7x and B = 5x
Now, given:
(R + 800) : (B + 2000) = 4 : 3 ⇒ 3(7x + 800) = 4(5x + 2000) ⇒ 21x + 2400 = 20x + 8000 ⇒ x = 5600
∴ Combined income of R and B = 7x + 5x = 12x = 12 × 5600 = Rs. 67,200
Hence, option (a).