A two-digit number is 7 times the sum of its two digits. The number that is formed by reversing its digits is 18 less than the original number. What is the number ?
A. 42
B. 52
C. 62
D. 72
Answer: Option A
Solution(By Examveda Team)
Let the ten's digit be x and the unit's digit be yThen, number = 10x + y
$$\eqalign{ & \therefore 10x + y = 7\left( {x + y} \right) \cr & \Leftrightarrow 3x = 6y \cr & \Leftrightarrow x = 2y \cr} $$
Number formed by reversing the digits = 10y + x
$$\eqalign{ & \therefore \left( {10x + y} \right) - \left( {10y + x} \right) = 18 \cr & \Leftrightarrow 9x - 9y = 18 \cr & \Leftrightarrow x - y = 2 \cr & \Leftrightarrow 2y - y = 2 \cr & \Leftrightarrow y = 2 \cr & {\text{So, }}x = 2y = 4 \cr} $$
Hence,
∴ Required number
= 10x + y
= 40 + 2
= 42
This Question Belongs to Arithmetic Ability >> Problems On Numbers
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After solving the question you find out that x= 2 and
y= 4 ,then while putting values in 10x+y how you made 10x 40 and y= 2
According to your values it should be 10x+y = 10×2+4
Which is equal to 24.