Which of the following alternative should be interchanged:
15 + 3 x 4 - 8 $\div$ 2 = 8 x 5 + 16 $\div$ 2 - 1

3 and 1

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15 and 5

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15 and 16

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3 and 5

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Solution

The correct option is D 3 and 5
1. Check alternative (I).
Given equation is 15 + 3 x 4 - 8 $\div$ 2 = 8 x 5 + 16 $\div$ 2 - 1.
On interchanging 3 and 1, we get
15 + 1 x 4 - 8 $\div$ 2 = 8 x 5 + 16 $\div$ 2 - 3
LHS = 15 + 1 x 4 - 8 $\div$ 2 = 15 + 4 - 4 = 19 - 4 = 15
RHS = 8 x 5 + 16 $\div$ 2 - 3 = 40 + 8 - 3 = 48 - 3 = 45
LHS $\neq$ RHS.
So, this option does not hold good.
2. Check alternative (2).
Given equation is 15 + 3 x 4 -8 $\div$ 2 = 8 x 5 + 16 $\div$ 2 - 1.
On interchanging 15 and 5,
we get 5 + 3 x 4 - 8 $\div$ 2 = 8 x 15 + 16 $\div$ 2 - 1.
LHS = 5 + 3 x 4 - 8 $\div$ 2 = 5 + 12 - 4 = 17 - 4 = 13
RHS = 8 x 15 + 16 $\div$ 2 - 1 = 120 + 8 - 1= 128 - 1= 127.
LHS $\neq$ RHS.
So, this option also does not hold good.
3. Check alternative (3).
Given equation is 15 + 3 x 4 -8 $\div$ 2 = 8 x 5 + 16 $\div$ 2 - 1.
On interchanging 15 and 16, we get
16 + 3 x 4 - 8 $\div$ 2 = 8 x 5 + 15 + 2 - 1
LHS = 16 + 3 x 4 - 8 $\div$ 2 = 16 + 12 - 4 = 28 - 4 = 24
RHS = 8 x 5 + 15 $\div$ 2 - 1 = 40 + 7.5 - 1 = 47.5 - 1 = 46.5.
LHS $\neq$ RHS.
So, this option also does not hold good.
4. Check alternative (4).
Given equation is 15 + 3 x 4 -8 $\div$ 2 = 8 x 5 + 16 $\div$ 2 - 1.
On interchanging 3 and 5, we get
15 + 5 x 4 - 8 $\div$ 2 = 8 x 3 + 16 $\div$ 2 - 1.
LHS = 15 + 5 x 4 - 8 $\div$ 2 = 15 + 20 - 4 = 35 - 4 = 31
RHS = 8 x 3 + 16 $\div$ 2 - 1 = 24 + 8 -1= 32 - 1 = 31
LHS = RHS.
So, this option holds good.

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Which of the following alternative should be interchanged:15 + 3 x 4 - 8 ÷ 2 = 8 x 5 + 16 ÷ 2 - 1

Which of the following alternative should be interchanged:
15 + 3 x 4 - 8 $\div$ 2 = 8 x 5 + 16 $\div$ 2 - 1