Solving Suhas's Division Error

This solution explains how to find the quotient Suhas obtained after making mistakes in the dividend and divisor during a division calculation.

Original Division Scenario

Let the original dividend be represented by D and the original divisor by d.

We are given that the correct quotient (Q) was 24 and the remainder (R) was 0.

The relationship between dividend, divisor, quotient, and remainder in division is given by the formula:

$$ D = d \times Q + R $$

Substituting the given values:

$$ D = d \times 24 + 0 $$

$$ D = 24d $$

This equation tells us that the original dividend was 24 times the original divisor.

Suhas's Mistaken Calculation

Suhas made two mistakes:

• He used a dividend (let's call it D') that was 10% less than the original dividend (D).
• He used a divisor (let's call it d') that was 20% less than the original divisor (d).

We can calculate these mistaken values:

Mistaken Dividend (D'):

$$ D' = D - (10\% \text{ of } D) $$

$$ D' = D - 0.10 \times D $$

$$ D' = D \times (1 - 0.10) $$

$$ D' = 0.90D $$

Mistaken Divisor (d'):

$$ d' = d - (20\% \text{ of } d) $$

$$ d' = d - 0.20 \times d $$

$$ d' = d \times (1 - 0.20) $$

$$ d' = 0.80d $$

Calculating the Obtained Quotient

Suhas performed the division using the mistaken dividend (D') and the mistaken divisor (d'). Let the new quotient he obtained be Q'.

The formula for the new quotient is:

$$ Q' = \frac{D'}{d'} $$

Now, we substitute the expressions for D' and d' that we found earlier:

$$ Q' = \frac{0.90D}{0.80d} $$

We know from the original problem that D = 24d. We substitute this into the equation for Q':

$$ Q' = \frac{0.90 \times (24d)}{0.80d} $$

The 'd' in the numerator and denominator cancels out:

$$ Q' = \frac{0.90 \times 24}{0.80} $$

$$ Q' = \frac{0.90}{0.80} \times 24 $$

Simplify the fraction $\frac{0.90}{0.80}$:

$$ Q' = \frac{9}{8} \times 24 $$

Now, perform the multiplication:

$$ Q' = 9 \times \frac{24}{8} $$

$$ Q' = 9 \times 3 $$

$$ Q' = 27 $$

Therefore, the quotient Suhas obtained was 27.