Meenu purchases two bags of rice of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the rice exact number of times.

The required maximum weight that can measure the weight of rice in both bags an exact number of times is the HCF of 75 and 69.

$\begin{array}{l} 69\overline{\smash{\big)}75\smash{\big(}}\phantom{}1 \ \phantom{x}\phantom{}\underline{-69} \ \phantom{{x^2 } 1)}6\overline{\smash{\big)}69\smash{\big(}}\phantom{}11 \ \phantom{{x} +(}\underline{-66} \ \phantom{{x^2 a} + 2)} 3\overline{\smash{\big)}6\smash{\big(}}\phantom{}2 \ \phantom{{x} +1xa(}\underline{-6} \ \phantom{{x^2 a} + 2x()} 0 \ \end{array}$

So, HCF of 75 and 69 = 3.

Hence, the maximum weight which can measure the rice exactly is 3 kg.