A woman reduces her weight in the ratio 7 : 5. What does her weight become if originally it was 91 kg?

Given, a woman reduces her weight in ratio 7 : 5 and original weight = 91 kg.

$\therefore \dfrac{\text{Original weight}}{\text{Reduced weight}} = \dfrac{7}{5} \\[0.5em] \Rightarrow \text{Reduced weight} = \dfrac{5}{7} \times \text{Original weight} \\[0.5em] \Rightarrow \text{Reduced weight} = \dfrac{5}{7} \times 91 \text{ kg} \\[0.5em] \Rightarrow \text{Reduced weight} = 5 \times 13 = 65 \text{ kg}$

Hence, the reduced weight of woman is 65 kg.