Question about the strong and weak acid

One fact we should be aware of that:
Strong acids ionize COMPLETELY and weak acids ionize PARTIALLY when dissolved in water.
So for strong acids, the equation is: HA --> H+ + A-
For weak acids, the equation is: HA <--> H+ + A-
Therefore, suppose that the dissociation constant of weak acid is Ka, and original concentration of acid is C, then at equilibrium:
[H+] = [A-] = x
[HA] = C - x
Hence the degree of ionization can be approximated as x/C by assuming that C >> x.
Therefore, from the relation, we can find out that as C decreases, the degree of ionization increases for weak acid.
Hence, when a weak acid is diluted, more H+ ions are given out (in amount) and so:
For a ten-fold dilution of weak acid, the rise in pH value is less than 1 since the increase in amount of H+ ions will make the dilution effect to be less than tn-fold.
Finally, we can compare, say, by a 100-fold dilution for each of the acids and make the judgement:
Strong acid: pH rises by 2 exactly (since no more H+ ions are given out)
Weak acid: pH rises by less than 2
So at that moment, pH of the diluted strong acid = 4 while pH of the diluted weak acid < 4 and this can be verified by pH paper colour inspection.

Where do you get this question from? im only a high school student so Ill try to answer your question at my level.
A strong acid will almost fully dissociate, when placed in water, and produce H ions from water. Whereas a weak acid only partially dissociate. The concentration of H ions is what influence the pH. So you should have different pH values from the two acids when placed in distilled water. If the concentration of the acid is known then by measuring the pH using the given indicators then you can tell its strong or weak.
Take for an example, a 0.1M solution of HCl has a pH of 1.00
a 0.1 M solution of CH3COOH has pH of 2.87.
Remind you about the indicators, because they have different ranges.
Litmus has a range of pH 5-8 it is red in acid and blue in alkali.
Phenolphthalein has a range of 8.2-10 and it is from colourless to pink.
Therefore you should use pH strip instead, which can tell you the pH value more accurately.
Hope I have helped you to some extent...it will be much easier if you are given a strong base though, then titration can solve the problem easily.