Let \( A \) be Adamu's monthly allowance.
According to the problem, Adamu spends \( \frac{3}{5} \) of his allowance on food and \( \frac{1}{4} \) on learning materials. The total amount he spends on both is:
\[ \frac{3}{5}A + \frac{1}{4}A \]
We are also told that this total spending is \( 33000 \) less than his allowance:
\[ \frac{3}{5}A + \frac{1}{4}A = A - 33000 \]
To solve this equation, first, we need to combine the fractions on the left-hand side. The least common multiple (LCM) of \( 5 \) and \( 4 \) is \( 20 \). We can rewrite the fractions:
\[ \frac{3}{5}A = \frac{3 \times 4}{5 \times 4}A = \frac{12}{20}A \] \[ \frac{1}{4}A = \frac{1 \times 5}{4 \times 5}A = \frac{5}{20}A \]
Now, combine the fractions:
\[ \frac{12}{20}A + \frac{5}{20}A = \frac{17}{20}A \]
Now, we can rewrite the equation:
\[ \frac{17}{20}A = A - 33000 \]
Next, we can multiply the entire equation by \( 20 \) to eliminate the fraction:
\[ 17A = 20A - 660000 \]
Rearranging the equation gives:
\[ 660000 = 20A - 17A \] \[ 660000 = 3A \]
Now, divide both sides by \( 3 \):
\[ A = \frac{660000}{3} = 220000 \]
Thus, Adamu's monthly allowance is \( \boxed{220000} \).
To verify, we can check the spending:
- Amount spent on food: \( \frac{3}{5} \times 220000 = 132000 \)
- Amount spent on learning materials: \( \frac{1}{4} \times 220000 = 55000 \)
- Total spending: \( 132000 + 55000 = 187000 \)
Now, check if this is indeed \( 33000 \) less than the allowance:
\[ 220000 - 33000 = 187000 \]
The calculations match, confirming that the monthly allowance is correct. Adamu’s monthly allowance is \( \boxed{220000} \).
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