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    Question

    There are five numbers β€˜a’, β€˜b’,

    β€˜c’, β€˜d’ and β€˜e’. The average of β€˜b’ and β€˜c’ is 390. The value of β€˜a’ is 40 more than 50% of β€˜d’. The value of β€˜e’ is 80 less than the value of β€˜b’. The value of β€˜d’ is 32 more than the 60% of β€˜e’. The value of β€˜c’ is 140 less than double the value of β€˜e’. As per the above given information, which of the following statements is/are correct? (i) The value of β€˜a’ is the multiple of 7. (ii) The value of β€˜d’ is completely divisible by 12. (iii) 25% of β€˜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 β€˜b’ and β€˜c’ is 390.

    (b+c)/2 = 390

    (b+c) = 780

    b = (780-c)Β  Β  Eq.(i)

    The value of β€˜e’ is 80 less than the value of β€˜b’.

    e = b-80

    Put the value of β€˜b’ from Eq.(i) in the above equation.

    e = (780-c)-80

    e = (700-c)Β  Β  Eq.(ii)

    The value of β€˜c’ is 140 less than double the value of β€˜e’.

    c = 2e-140

    Put the value of β€˜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 β€˜c’ in Eq.(ii).

    e = (700-420)

    e = 280

    Put the value of β€˜c’ in Eq.(i).

    b = (780-420)

    b = 360

    The value of β€˜d’ is 32 more than the 60% of β€˜e’.

    d = 32 + 60% of e

    Put the value of β€˜e’ in the above equation.

    d = 32 + 60% of 280

    d = 32 + 60% of 280

    d = 32 + 168

    d = 200

    The value of β€˜a’ is 40 more than 50% of β€˜d’.

    a = 50% of d + 40

    Put the value of β€˜d’ in the above equation.

    a = 50% of 200 + 40

    a = 100 + 40

    a = 140

    Now we have the values of β€˜a’, β€˜b’, β€˜c’, β€˜d’ and β€˜e’.

    (i) The value of β€˜a’ is the multiple of 7.

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

    (ii) The value of β€˜d’ is completely divisible by 12.

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

    (iii) 25% of β€˜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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