Mr. Manohar gave 20% part of his income to his elder son and 30% part to his younger son. He gave 10% of the balance as donation to a school. He still had Rs. 1,80,000 for himself. What was Mr. Manoha

You're on a roll — here are the solutions to the questions. 1) Mr. Manohar gave 20% part of his income to his elder son and 30% part to his younger son. He gave 10% of the balance as donation to a school. He still had Rs. 1,80,000 for himself. What was Mr. Manohar's income? Step 1: Let Mr. Manohar's total income be I. Amount given to elder son = 20\% of I = 0.20I Amount given to younger son = 30\% of I = 0.30I Step 2: Calculate the total percentage of income given to his sons. Total percentage given to sons = 20\% + 30\% = 50\% Total amount given to sons = 0.20I + 0.30I = 0.50I Step 3: Calculate the balance remaining after giving to his sons. Balance = Total Income - Amount given to sons Balance = I - 0.50I = 0.50I Step 4: Calculate the amount donated to the school. Donation = 10\% of the balance Donation = 0.10 × (0.50I) = 0.05I Step 5: Calculate the amount remaining for himself. Amount remaining = Balance - Donation Amount remaining = 0.50I - 0.05I = 0.45I Step 6: Set up the equation with the given remaining amount and solve for I. We are given that he still had Rs. 1,80,000 for himself. 0.45I = 1,80,000 I = (1,80,000)/(0.45) To simplify the division, multiply the numerator and denominator by 100: I = (1,80,000 × 100)/(0.45 × 100) I = (18,000,000)/(45) I = 400,000 Mr. Manohar's total income was Rs. 4,00,000. Mr. Manohar's income was Rs. 4,00,000. 2) If (x+3) : (x+11) = (x-2) : (x+1), then find the value of x. Step 1: Write the proportion as a fraction. (x+3)/(x+11) = (x-2)/(x+1) Step 2: Cross-multiply the terms. (x+3)(x+1) = (x-2)(x+11) Step 3: Expand both sides of the equation. Left side: x(x+1) + 3(x+1) = x^2 + x + 3x + 3 = x^2 + 4x + 3 Right side: x(x+11) - 2(x+11) = x^2 + 11x - 2x - 22 = x^2 + 9x - 22 Step 4: Set the expanded expressions equal to each other. x^2 + 4x + 3 = x^2 + 9x - 22 Step 5: Solve for x. Subtract x^2 from both sides: 4x + 3 = 9x - 22 Subtract 4x from both sides: 3 = 5x - 22 Add 22 to both sides: 3 + 22 = 5x 25 = 5x Divide by 5: x = (25)/(5) x = 5 x = 5 Got more? Send 'em!