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Q.

If the sum of the repeating decimals 0.353535…+0.252525…   is written as a fraction in lowest terms, the product of the numerator and denominator is:


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a

2475

b

680

c

670

d

660

answer is D.

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Detailed Solution

Concep- We will first write 0.353535…   and 0.252525…   in the form of p q   where q≠0   separately. For doing that, we will express the first term as x=0.353535…  , then multiply with 100 as 100x=35.353535   and then express it as 100x=35+0.353535  . Now, again this can be written as 100x=35+x  . Now, we can get x   in the form of a fraction. In a similar manner, we will carry out this process again for the second term. Then sum these two values in fractional form. The percent we ultimately achieve will be the one we need. The needed result is then obtained by multiplying its numerator and denominator.
0.353535…+0.252525…=0.6060…..  
 Let x=0.6060……  
100x=60.6060…  
100x−x=60  
99x=60  
x= 60 99 = 20 33  Numerator =20   and Denominator =33  
Their product =33×20=660  
Hence, the correct answer is option 4.
 
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