Maths-
General
Easy

Question

The number y is 20% greater than the number x. The number z is 20% less than y. The number z is how many times x?

The correct answer is: 0.96


    Hint:-
    We will formulate equations for the conditions mentioned in the question and simplify the same to finds the answer.
    Step-by-step solution:-
    y = x + 20% of x
    ∴ y = x + 20 over 100 cross times x
    ∴ y = x + 1 fifth x
    ∴ y = 5 over 5 x + 1 fifth x
    ∴ y = fraction numerator left parenthesis 5 plus 1 right parenthesis over denominator 5 space x end fraction
    ∴ y = 6 over 5 x ----------------------------------- (Equation i)
    z = y - 20% of y
    ∴ z = y - 20 over 100 cross times y
    ∴ z = y - 1 fifth y
    ∴ z = 5 over 5 y - 1 fifth y
    ∴ z =fraction numerator left parenthesis 5 minus 1 right parenthesis over denominator 5 space y end fraction
    ∴ z = 4 over 5 y
    ∴ z ×5 over 4 = y---------------------------------- (Dividing both sides by 4 over 5)
    5 over 4 z = y ------------------------------------ (Equation ii)
    Substituting Equation ii in Equation i, we get
    y = 6 over 5 x
    5 over 4 z = 6 over 5 x
    ∴ z = 6 over 5 × 4 over 5 × x-------------------------------- (Dividing both sides by 5 over 4)
    ∴ z = 24 over 25 x
    ∴ z = 24 over 25 x or z = 0.96 x
    Final Answer:-
    The number z is 24 over 25 times or 0.96 times the number x.
    Note:-
    Alternatively, we can assume z to be 100,
    ∴ z = y - 20% y
    ∴ 100 = 80% y
    ∴ 100 = 80 over 100 cross times y
    ∴ v100cross times100 over 80 = y
    125 = y ----------------------------- (Equation i)
    Also, y = x + 20% x
    ∴ y = 120% x
    ∴ 125 = 120 over 100× x --------------------------- (From Equation i)
    ∴ 125×100 over 120 = x
    ∴ 104.17 = x--------------------- (Equation ii)
    Now, z over x = fraction numerator 100 over denominator 104.17 end fraction
    ∴ z over x = 0.96
    ∴ z =96 over 100 cross times x
    ∴ z = 24 over 25 cross times x or z = 0.96 × x

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