Mr. Manohar gave 20% part of his income to his elder son and 30% part to his younger son. He gave 10% of the…

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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

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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?

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 $I = 0.30I$
Calculate the total percentage of income given to his sons.
Total percentage given to sons = $20\% + 30\% = 50\%$
Total amount given to sons = $0.20I + 0.30I = 0.50I$
Calculate the balance remaining after giving to his sons.
Balance = Total Income - Amount given to sons
Balance = $I - 0.50I = 0.50I$
Calculate the amount donated to the school.
Donation = $10\%$ of the balance
Donation = $0.10 \times (0.50I) = 0.05I$
Calculate the amount remaining for himself.
Amount remaining = Balance - Donation
Amount remaining = $0.50I - 0.05I = 0.45I$
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.
$0.45I = 1,80,000$ $I = \frac{1,80,000}{0.45}$
To simplify the division, multiply the numerator and denominator by 100:
$I = \frac{1,80,000 \times 100}{0.45 \times 100}$ $I = \frac{18,000,000}{45}$ $I = 400,000$
Mr. Manohar's total income was Rs. 4,00,000.
$\boxed{\text{Mr. Manohar's income was Rs. 4,00,000.}}$
2) If $(x+3) : (x+11) = (x-2) : (x+1)$ , then find the value of $x$ .
Write the proportion as a fraction.
$\frac{x+3}{x+11} = \frac{x-2}{x+1}$
Cross-multiply the terms.
$(x+3)(x+1) = (x-2)(x+11)$
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:
$x(x+11) - 2(x+11) = x^2 + 11x - 2x - 22 = x^2 + 9x - 22$
Set the expanded expressions equal to each other.
$x^2 + 4x + 3 = x^2 + 9x - 22$
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:
$x = \frac{25}{5}$ $x = 5$ $\boxed{x = 5}$

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

Step-by-step solution

Let Mr.

Calculate the total percentage of income given to his sons.

Calculate the balance remaining after giving to his sons.

Calculate the amount donated to the school.

Calculate the amount remaining for himself.

Set up the equation with the given remaining amount and solve for $I$ .

Write the proportion as a fraction.

Cross-multiply the terms.

Expand both sides of the equation.

Set the expanded expressions equal to each other.

Solve for $x$ .

Still stuck on this one?

More Mathematics Questions

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

Step-by-step solution

Let Mr.

Calculate the total percentage of income given to his sons.

Calculate the balance remaining after giving to his sons.

Calculate the amount donated to the school.

Calculate the amount remaining for himself.

Set up the equation with the given remaining amount and solve for III.

Write the proportion as a fraction.

Cross-multiply the terms.

Expand both sides of the equation.

Set the expanded expressions equal to each other.

Solve for xxx.

Still stuck on this one?

More Mathematics Questions

Set up the equation with the given remaining amount and solve for $I$ .

Solve for $x$ .