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    Question

    There are five numbers ‘a’, ‘b’,

    ‘c’, ‘d’ and ‘e’. The average of ‘b’ and ‘c’ is 390. The value of ‘a’ is 40 more than 50% of ‘d’. The value of ‘e’ is 80 less than the value of ‘b’. The value of ‘d’ is 32 more than the 60% of ‘e’. The value of ‘c’ is 140 less than double the value of ‘e’. As per the above given information, which of the following statements is/are correct? (i) The value of ‘a’ is the multiple of 7. (ii) The value of ‘d’ is completely divisible by 12. (iii) 25% of ‘c’ is equal to 115.
    A Only (ii) Correct Answer Incorrect Answer
    B Only (i) Correct Answer Incorrect Answer
    C Only (ii) and (iii) Correct Answer Incorrect Answer
    D Only (i) and (iii) Correct Answer Incorrect Answer

    Solution

    The average of ‘b’ and ‘c’ is 390.

    (b+c)/2 = 390

    (b+c) = 780

    b = (780-c)    Eq.(i)

    The value of ‘e’ is 80 less than the value of ‘b’.

    e = b-80

    Put the value of ‘b’ from Eq.(i) in the above equation.

    e = (780-c)-80

    e = (700-c)    Eq.(ii)

    The value of ‘c’ is 140 less than double the value of ‘e’.

    c = 2e-140

    Put the value of ‘e’ from Eq.(ii) in the above equation.

    c = 2(700-c)-140

    c = 1400-2c-140

    c+2c = 1400-140

    3c = 1260

    c = 420

    Put the value of ‘c’ in Eq.(ii).

    e = (700-420)

    e = 280

    Put the value of ‘c’ in Eq.(i).

    b = (780-420)

    b = 360

    The value of ‘d’ is 32 more than the 60% of ‘e’.

    d = 32 + 60% of e

    Put the value of ‘e’ in the above equation.

    d = 32 + 60% of 280

    d = 32 + 60% of 280

    d = 32 + 168

    d = 200

    The value of ‘a’ is 40 more than 50% of ‘d’.

    a = 50% of d + 40

    Put the value of ‘d’ in the above equation.

    a = 50% of 200 + 40

    a = 100 + 40

    a = 140

    Now we have the values of ‘a’, ‘b’, ‘c’, ‘d’ and ‘e’.

    (i) The value of ‘a’ is the multiple of 7.

    The value of ‘a’ is 140 which is the multiple of 7. So the above given statement is correct.

    (ii) The value of ‘d’ is completely divisible by 12.

    The value of ‘d’ is 200 which is not completely divisible by 12. So the above given statement is not correct.

    (iii) 25% of ‘c’ is equal to 115.

    25% of c = 25% of 420 = 105

    So the above given statement is not correct.

    Thus we can say that only statement (i) is correct.

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