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 + x
∴ y = x + x
∴ y = x + x
∴ y =
∴ y = x ----------------------------------- (Equation i)
z = y - 20% of y
∴ z = y -
∴ z = y - y
∴ z = y - y
∴ z =
∴ z = y
∴ z × = y---------------------------------- (Dividing both sides by )
∴ z = y ------------------------------------ (Equation ii)
Substituting Equation ii in Equation i, we get
y = x
∴ z = x
∴ z = × × x-------------------------------- (Dividing both sides by )
∴ z = x
∴ z = x or z = 0.96 x
Final Answer:-
The number z is 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 =
∴ v100 = y
125 = y ----------------------------- (Equation i)
Also, y = x + 20% x
∴ y = 120% x
∴ 125 = × x --------------------------- (From Equation i)
∴ 125× = x
∴ 104.17 = x--------------------- (Equation ii)
Now, =
∴ = 0.96
∴ z = x
∴ z = x or z = 0.96 × x
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