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A student finds the average of 10, 2 digits numbers. If the digits of one of the numbers interchanged, the average increases by 3.6. The difference between the digits of the 2 digits number is :
Answer & Solution
Correct Answer:
Option
A
According to the question,
Let as consider by mistake he writes 10th number with its digits interchanged
∴ $$\frac{{10x + y - \left( {10y + x} \right)}}{{10}} = 3.6$$
∴ In these remaining nine numbers are same and they cancel out
$$\eqalign{ & \Rightarrow \frac{{10x + y - \left( {10y + x} \right)}}{{10}} = 3.6 \cr & \Rightarrow 9x - 9y = 36 \cr & \Rightarrow x - y = 4 \cr} $$
Let as consider by mistake he writes 10th number with its digits interchanged
∴ $$\frac{{10x + y - \left( {10y + x} \right)}}{{10}} = 3.6$$
∴ In these remaining nine numbers are same and they cancel out
$$\eqalign{ & \Rightarrow \frac{{10x + y - \left( {10y + x} \right)}}{{10}} = 3.6 \cr & \Rightarrow 9x - 9y = 36 \cr & \Rightarrow x - y = 4 \cr} $$
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LoginAvg increased =3.6 x 10 = 36
Trick = Divide the total decreased or increased average by 9 to get the answer
Now divide 36/9 = 4 Ans