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CTET Paper II (Mathematics and Science) 1 Jan 2022 Solved Paper

Question : 43 of 150

Marks: +1, -0

y-\frac{y-1}{2}=1-\frac{y-2}{3}

\frac{5y+7}{2}

Solution:

Concept:

To solve an equation with fractions, eliminate denominators by finding a common denominator and then cross-multiplying.

Explanation:

Start with

y - \frac{y-1}{2} = 1 - \frac{y-2}{3}

Combine terms on each side: Left side becomes

\frac{2y - (y-1)}{2} = \frac{y+1}{2}

. Right side becomes

\frac{3 - (y-2)}{3} = \frac{5-y}{3}

Now equate:

\frac{y+1}{2} = \frac{5-y}{3}

Cross-multiply:

3(y+1) = 2(5-y)

Expand:

3y + 3 = 10 - 2y

Bring like terms together:

3y + 2y = 10 - 3

→

5y = 7

→

y = \frac{7}{5}

Now compute

\frac{5y+7}{2}

: Substitute

y

→

\frac{5 \times \frac{7}{5} + 7}{2} = \frac{7 + 7}{2} = \frac{14}{2} = 7

Answer:

D. 7

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