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Worked Examples

Example-1

Interchange the symbols ‘+’ and ‘÷’; numbers 2 and 4. Find out the alternative which is correct.

  1. 2 + 4 ÷ 3 = 3.
  2. 4 + 2 ÷ 6 = 1.5.
  3. 4 ÷ 2 + 3 = 4.
  4. 2 + 4 ÷ 6 = 8.

Solution

Consider the alternatives one by one. Interchange the symbols and numbers as suggested in the question and check whether the equation holds good.

  1. Consider option (1).
     
    2 + 4 ÷ 3 = 3.
     
    On effecting interchange of symbols and numbers, the equation becomes
     
    4 ÷ 2 + 3 = 3
     
    Check whether this equation is correct.
     
    LHS = 4 ÷ 2 + 3 =2 + 3 = 5 ≠ 3.
     
    So, this option does not hold good.
  2. Now, consider option (2).
     
    4 + 2 ÷ 6 = 1.5.
     
    On effecting interchange of symbols and numbers, the equation becomes
     
    2 ÷ 4 + 6 = 1.5.
     
    Check whether this equation is correct.
     
    LHS = 2 ÷ 4 + 6 = 0.5 + 6 = 6.5 ≠ 1.5.
     
    So, this option also does not hold good.
  3. Next, consider option (3).
     
    4 ÷ 2 + 3 = 4.
     
    On effecting interchange of symbols and numbers, the equation becomes
     
    2 + 4 ÷ 3 = 2 (Note: Even 4 in the answer part changes into 2.)
     
    Check whether this equation is correct.
     
    LHS = 2 + 4/3 ≠ 2
     
    So, this option also does not hold good.
  4. Finally, consider option (4).
     
    2 + 4 ÷ 6 = 8.
     
    On effecting interchange of symbols and numbers, the equation becomes
     
    4 ÷ 2 + 6 = 8
     
    Check whether this equation is correct.
     
    LHS = 4 ÷ 2 + 6 = 2 + 6 = 8 = RHS. This is correct.

Answer: (4)
 

 

Example-2

Which one of the four interchanges in symbols and numbers would make the given equation correct?

 

Given equation: 3 + 5 - 2 = 4

  1. + and – ; 2 and 3
  2. + and –; 2 and 5
  3. + and –; 3 and 5
  4. None of these

Solution

Check every alternative by interchanging the symbols and numbers in the given equation.

  1. On interchanging the symbols and numbers as given in alternative (1) the given equation becomes
     
    2 - 5 + 3 = 4
     
    LHS = 2 - 5 + 3 = 5 – 5 = 0 ≠ 4.
     
    So, this option does not hold good.
  2. On interchanging the symbols and numbers as given in alternative (2), the given equation becomes
     
    3 - 2 + 5 = 4
     
    LHS = 3 - 2 + 5 = 8 – 2 = 6 ≠ 4.
     
    So, this option also does not hold good.
  3. On interchanging the symbols and numbers as given in alternative (3) the given equation becomes
     
    5 - 3 + 2 = 4
     
    LHS = 5 - 3 + 2 = 7 – 3 = 4 = RHS.
     
    So, this option holds good.

Answer: (3)
 

 

Example-3

Interchange the symbols - and ×; and the numbers 15 and 18. Find the correct alternative.

  1. (20 × 10) + 15 = 25.
  2. (25 - 3) + 18 = 93.
  3. (40 ÷ 4) - 18 = 180.
  4. (64 × 10) ÷ 15 = 3.

Solution

Check every alternative.

  1. (20 × 10) + 15 = 25.
     
    After interchanging symbols and numbers as suggested in the question, the equation becomes
     
    (20 - 10) + 18 = 25.
     
    LHS = (20 - 10) + 18 = 10 + 18 = 28 ≠ 25.
     
    So, this option does not hold good.
  2. (25 - 3) + 18 = 93.
     
    After interchanging symbols and numbers as suggested in the question, the equation becomes
     
    (25 × 3) + 15 = 93
     
    LHS = (25 × 3) + 15 = 75 + 15 = 90 ≠ 93.
     
    So, this option also does not hold good.
  3. (40 ÷ 4) - 18 = 180.
     
    After interchanging symbols and numbers as suggested in the question, the equation becomes
     
    (40 ÷ 4) × 15 = 180
     
    LHS = (40 ÷ 4) × 15 = 10 × 15 = 150 ≠ 180.
     
    So, this option also does not hold good.
  4. (64 × 10) ÷ 15 = 3.
     
    After interchanging symbols and numbers as suggested in the question, the equation becomes
     
    (64 - 10) ÷ 18 = 3.
     
    LHS = (64 - 10) ÷ 18 = 54 ÷ 18 =3 = RHS
     
    So, this option is correct.

Answer: (4)
 

 

Example-4

Interchange - and × ; 3 and 6. Which of the following four options becomes correct?

  1. 6 - 3 × 2 = 9.
  2. 3 × 6 - 4 = 14.
  3. 3 × 6 - 4 = 33.
  4. 3 - 6 × 8 = 10.

Solution

Check every alternative.

  1. 6 - 3 × 2 = 9.
     
    On interchanging - and × ; 3 and 6, the equation becomes
     
    3 × 6 - 2 = 9.
     
    LHS = 3 × 6 - 2 = 18 - 2 = 16 ≠ 9.
     
    So, this option does not hold good.
  2. 3 × 6 – 4 = 14.
     
    On interchanging - and × ; 3 and 6, the equation becomes
     
    6 – 3 × 4 = 14.
     
    LHS = 6 – 3 × 4 = 6 – 12 = – 6 ≠ 14.
     
    So, this option also does not hold good.
  3. 3 × 6 – 4 = 33.
     
    On interchanging - and × ; 3 and 6, the equation becomes
     
    6 – 3 × 4 = 33.
     
    LHS = 6 – 3 × 4 = 6 – 12 = – 6 ≠ 33.
     
    So, this option also does not hold good.
  4. 3 - 6 × 8 = 10.
     
    On interchanging - and × ; 3 and 6, the equation becomes
     
    6 × 3 - 8 = 10
     
    LHS = 6 × 3 - 8 = 18 – 8 = 10 = RHS
     
    So, this option is correct.

Answer: (4)
 

 

Example-5

Which of the two signs (symbols) you have to interchange to make the equation correct?

 

10 + 10 ÷ 10 - 10 × 10 = 10.

  1. + and –
  2. + and ÷
  3. + and ×
  4. ÷ and ×.

Solution
  1. Given equation is 10 + 10 ÷ 10 - 10 × 10 = 10.
     
    On interchanging the symbols as suggested in option (1), the equation becomes;
     
    10 - 10 ÷ 10 + 10 × 10 = 10
     
    LHS = 10 - 10 ÷ 10 + 10 × 10 = 10 - 1 + 100 = 109 ≠ 10
     
    So, this option does not hold good.
  2. Given equation is 10 + 10 ÷ 10 - 10 × 10 = 10.
     
    On interchanging the symbols as suggested in option (2), the equation becomes;
     
    10 ÷ 10 + 10 - 10 × 10 = 10
     
    LHS = 10 ÷ 10 + 10 - 10 × 10 = 1 + 10 - 100 = - 89 ≠ 10
     
    So, this option also does not hold good.
  3. Given equation is 10 + 10 ÷ 10 - 10 × 10 = 10.
     
    On interchanging the symbols as suggested in option (3), the equation becomes;
     
    10 × 10 ÷ 10 -10 + 10 = 10.
     
    LHS = 10 × 10 ÷ 10 -10 + 10 = 10 × 1 - 10 + 10 = 10- 10 + 10 = 20 - 10 = 10 = RHS.
     
    This is correct.
  4. Given equation is 10 + 10 ÷ 10 - 10 × 10 = 10.
     
    On interchanging the symbols as suggested in option (4), the equation becomes;
     
    10 + 10 × 10 - 10 ÷ 10 = 10.
     
    LHS = 10 + 10 × 10 - 10 ÷ 10 = 10 + 100 - 1 = 109 ≠ 10.
     
    So, this option also does not hold good.

Answer: (3)
 

The two expressions on either side of the sign (=) will have the same value, if two terms on either side or on the same side are interchanged. Choose the correct terms to be interchanged from the alternatives given below the equation.
 

 

Example-6

5 + 3 × 6 - 4 ÷ 2 = 4 × 3 - 10 ÷ 2 + 7

  1. 5 and 7.
  2. 6 and 10.
  3. 4 and 7.
  4. None of these.

Solution
  1. Check alternative (1).
     
    Given equation is 5 + 3 × 6 - 4 ÷ 2 = 4 × 3 - 10 ÷ 2 + 7.
     
    On interchanging 5 and 7, we get
     
    7 + 3 × 6 - 4 ÷ 2 = 4 × 3 - 10 ÷ 2 + 5
     
    LHS = 7 + 3 × 6 - 4 ÷ 2 RHS = 4 × 3 - 10 ÷ 2 + 5
     
    = 7 + 18 - 2 = 12 - 5 + 5
     
    = 25 - 2 = 17 - 5
     
    = 23 = 12.
     
    LHS ≠ RHS.
     
    So, this option does not hold good.
  2. Check alternative (2).
     
    Given equation is 5 + 3 × 6 - 4 ÷ 2 = 4 × 3 - 10 ÷ 2 + 7.
     
    On interchanging 6 and 10, we get
     
    5 + 3 × 10 - 4 ÷ 2 = 4 × 3 - 6 ÷ 2 + 7.
     
    LHS = 5 + 3 × 10 - 4 ÷ 2 RHS = 4 × 3 - 6 ÷ 2 + 7
     
    = 5 + 30 - 2 = 12 - 3 + 7
     
    = 35 - 2 = 19 - 3
     
    = 33 = 16.
     
    LHS ≠ RHS.
     
    So, this option also does not hold good.
  3. Check alternative (3).
     
    Given equation is 5 + 3 × 6 - 4 ÷ 2 = 4 × 3 - 10 ÷ 2 + 7.
     
    On interchanging 4 and 7, we get
     
    5 + 3 × 6 - 7 ÷ 2 = 7 × 3 - 10 ÷ 2 + 4
     
    LHS = 5 + 18 - 3.5 RHS = 21 - 5 + 4
     
    = 23 - 3.5 = 25 - 5
     
    = 19.5 = 20
     
    LHS ≠ RHS.
     
    So, this option also does not hold good.

Answer: (4) None of these.
 

 

Example-7

15 + 3 × 4 - 8 ÷ 2 = 8 × 5 + 16 ÷ 2 - 1

  1. 3 and 1.
  2. 15 and 5.
  3. 15 and 16.
  4. 3 and 5.

Solution
  1. Check alternative (1).
     
    Given equation is 15 + 3 × 4 - 8 ÷ 2 = 8 × 5 + 16 ÷ 2 - 1.
     
    On interchanging 3 and 1, we get
     
    15 + 1 × 4 - 8 ÷ 2 = 8 × 5 + 16 ÷ 2 - 3
     
    LHS = 15 + 1 × 4 - 8 ÷ 2 RHS = 8 × 5 + 16 ÷ 2 - 3
     
    = 15 + 4 - 4 = 40 + 8 - 3
     
    = 19 - 4 = 48 - 3
     
    = 15 = 45
     
    LHS ≠ RHS.
     
    So, this option does not hold good.
  2. Check alternative (2).
     
    Given equation is 15 + 3 × 4 - 8 ÷ 2 = 8 × 5 + 16 ÷ 2 - 1.
     
    On interchanging 15 and 5, we get
     
    5 + 3 × 4 – 8 ÷ 2 = 8 × 15 + 16 ÷ 2 – 1.
     
    LHS = 5 + 3 × 4 – 8 ÷ 2 RHS = 8 × 15 + 16 ÷ 2 – 1.
     
    = 5 + 12 - 4 = 120 + 8 - 1.
     
    = 17 - 4 = 128 - 1.
     
    = 13 = 127.
     
    LHS ≠ RHS.
     
    So, this option also does not hold good.
  3. Check alternative (3).
     
    Given equation is 15 + 3 × 4 - 8 ÷ 2 = 8 × 5 + 16 ÷ 2 - 1.
     
    On interchanging 15 and 16, we get
     
    16 + 3 × 4 – 8 ÷ 2 = 8 × 5 + 15 ÷ 2 – 1.
     
    LHS = 16 + 3 × 4 – 8 ÷ 2 RHS = 8 × 5 + 15 ÷ 2 – 1.
     
    = 16 + 12 - 4 = 40 + 7.5 - 1.
     
    = 28 - 4 = 47.5 - 1.
     
    = 24 = 46.5.
     
    LHS ≠ RHS.
     
    So, this option also does not hold good.
  4. Check alternative (4).
     
    Given equation is 15 + 3 × 4 - 8 ÷ 2 = 8 × 5 + 16 ÷ 2 - 1.
     
    On interchanging 3 and 5, we get
     
    15 + 5 × 4 - 8 ÷ 2 = 8 × 3 + 16 ÷ 2 - 1.
     
    LHS = 15 + 5 × 4 - 8 ÷ 2 RHS = 8 × 3 + 16 ÷ 2 - 1.
     
    = 15 + 20 - 4 = 24 + 8 - 1.
     
    = 35 - 4 = 32 - 1.
     
    = 31 = 31.
     
    LHS = RHS.
     
    So, this option holds good.

Answer: (4).
 





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