Question

A school girl spend 1/4 of her pocket money on books and 1/3 of it on dress . If this adds up to 4200, how much is her pocket money.

Answer 1

Let the total pocket money of the school girl be \( x \).

According to the problem, she spends \( \frac{1}{4} \) of her pocket money on books and \( \frac{1}{3} \) of it on dresses. The total amount spent on books and dresses is given as 4200.

We can express this as an equation:

\[
\frac{1}{4}x + \frac{1}{3}x = 4200
\]

To solve this equation, we first need to find a common denominator for the fractions. The least common multiple of 4 and 3 is 12. Therefore, we can rewrite the fractions as follows:

\[
\frac{1}{4}x = \frac{3}{12}x \quad \text{and} \quad \frac{1}{3}x = \frac{4}{12}x
\]

Now substituting these into the equation:

\[
\frac{3}{12}x + \frac{4}{12}x = 4200
\]

Combining the fractions:

\[
\frac{3 + 4}{12}x = 4200
\]

This simplifies to:

\[
\frac{7}{12}x = 4200
\]

Next, we can solve for \( x \) by multiplying both sides by \( \frac{12}{7} \):

\[
x = 4200 \times \frac{12}{7}
\]

Calculating this:

\[
x = 4200 \times \frac{12}{7} = 4200 \times 1.714285714285714 = 7200
\]

Thus, her total pocket money is:

\[
\boxed{7200}
\]