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Madhu has three friends; Sonam, Divya and Radha. Ratio of monthly income of Sonam and Divya is 5 : 6 respectively and the ratio of monthly income of Radha and Divya is 4 : 3 respectively. Monthly income of Madhu is twice that of total monthly income of all her three friends. If monthly income of Madhu is Rs 26600 then what is the highest monthly income of any of her friends?

Madhu has three friends; Sonam, Divya and Radha. Ratio of monthly income of Sonam and Divya is 5 : 6 respectively and the ratio of monthly income of Radha and Divya is 4 : 3 respectively. Monthly income of Madhu is twice that of total monthly income of all her three friends. If monthly income of Madhu is Rs 26600 then what is the highest monthly income of any of her friends? Correct Answer Rs. 5600

Let the income of Sonam and Divya be Rs 5n and 6n respectively.

According to the question

ratio of income of Radha and Divya = 4 : 3 = 8 : 6

Hence ratio of income of Sonam, Divya and Radha = 5 : 6 : 8

Now sum of their total income = Rs (5n + 6n + 8n) = Rs. 19n

According to the question income of Madhu = Rs (2 × 19n) = Rs 38n

Hence: 38n = 26600

⇒ n = 700

∴ From the ratio it is clear that the income of Radha is highest amongst all the three friends of Madhu hence total income of Radha = Rs (8 × 700) = Rs 5600

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