The monthly incomes of two friends Mohan and David, are in the ratio 5 : 8, respectively, and each of them saves ₹75,000 every month.
The monthly incomes of two friends Mohan and David, are in the ratio 5 : 8, respectively, and each of them saves ₹75,000 every month. If the ratio of their monthly expenditure is 1 : 4, find the monthly income of Mohan(in ₹).
दो मित्र, मोहन और डेविड की मासिक आय क्रमशः 5 : 8 के अनुपात में है और उनमें से प्रत्येक हर महीने ₹75,000 बचत करता है। यदि उनके मासिक व्यय का अनुपात 1 : 4 है, तो मोहन की मासिक आय (₹ में) ज्ञात कीजिए।
Detailed Solution & Logic
93,750
Let the monthly incomes of Mohan and David be $5x$ and $8x$ respectively.
Let their monthly expenditures be $E_M$ and $E_D$.
We are given:
-
Each saves ₹75,000 → Income − Expenditure = Savings
$5x - E_M = 75000 \quad ...(1)$
$8x - E_D = 75000 \quad ...(2)$
-
Ratio of expenditures = 1 : 4 → $E_M : E_D = 1 : 4$ → $E_D = 4 E_M$
Step 1: Substitute $E_D = 4 E_M$ in (2)
$8x - 4E_M = 75000$
From (1): $E_M = 5x - 75000$
Substitute into above:
$8x - 4(5x - 75000) = 75000$
$8x - 20x + 300000 = 75000$
$-12x + 300000 = 75000$
$-12x = -225000$
$x = 18750$
Step 2: Mohan’s monthly income
$5x = 5 \cdot 18750 = 93750$
Answer: ₹93,750
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