UPTET Paper 2 Math and Science Model Test 5

Concept:When two fractions are equal, cross-multiply to eliminate the denominators and form a linear equation.Explanation:Start with the given proportion: $\frac{1-9y}{19-3y} = \frac{5}{8}$.Cross-multiply: $8 \times (1 - 9y) = 5 \times (19 - 3y)$.Expand both sides: $8 - 72y = 95 - 15y$.Bring all $y$ terms to one side and constants to the other: $-72y + 15y = 95 - 8$.Simplify: $-57y = 87$.Divide both sides by $-57$: $y = \frac{87}{-57}$.Reduce the fraction by dividing numerator and denominator by 3: $y = -\frac{29}{19}$.Answer:The value of $y$ is $-\frac{29}{19}$, which matches option C.