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Q.

What is the value of y in $\frac{y - 1}{3} - \frac{y - 2}{4} = 1$ ?

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a

11

b

10

c

12

d

13

answer is B.

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Detailed Solution

Given,

\frac{y - 1}{3} - \frac{y - 2}{4} = 1

.
The prime factorisation of 3 is 3.
The prime factorisation of 4 is

2 \times 2

.
Hence, the LCM between 3 and 4 is

3 \times 2 \times 2 = 12

.

\frac{y - 1}{3} - \frac{y - 2}{4} = 1

\frac{4 (y - 1) - 3 (y - 2)}{12} = 1

\frac{4 y - 4 - 3 y + 6}{12} = 1

\frac{y + 2}{12} = 1

y + 2 = 12

y = 10
LHS =

\frac{y - 1}{3} - \frac{y - 2}{4}

= \frac{10 - 1}{3} - \frac{10 - 2}{4}

= 1

RHS = 1
LHS = RHS
So, the value of y is 10.
Hence, option 2 is correct.

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