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Archit3110
The ratio of a two-digit positive integer to a number formed by reversing its digits is 4:7. Which of the following is the sum of all the numbers of all such pairs?

A. 99
B. 132
C. 198
D. 282
E. 330

given
(10a+b)/(10b+a)= 4/7
we get
2a=b
so
value of integers ( 12,21) ( 24,42) ( 36,63) ( 48,84)
total sum of all integers = 330
IMO E


Can you please explain the highlighted step?


a and b represent the tens and units digits of the original two-digit number. Since 2a = b, the valid pairs of digits are (1, 2), (2, 4), (3, 6), and (4, 8). This gives the numbers 12, 24, 36, and 48, with their reversals 21, 42, 63, and 84.
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