The ratio between a two-digit number and the sum of digits of that num

1.	The ratio between a two-digit number and the sum of digits of that number is 4 : 1. If the digit in the unit place is 3 more than the digit in the tenth place. What is that number ? A) 36B) 49 C) 86 D) 92
Answer» Correct option is (A) 36 Let the number be ab or (10a+b). Given that ratio of two-digit number and the sum of digit of that number is 4 : 1. \(\therefore\) \(\frac{10a+b}{a+b}=\frac41\) \(\Rightarrow\) 10a+b = 4a+4b \(\Rightarrow\) 6a = 3b \(\Rightarrow\) b = 2a _____________(1) According to \(2^{nd}\) condition, we have b = a+3 _____________(2) \(\Rightarrow\) 2a = a+3 (From (1)) \(\Rightarrow\) a = 3 \(\therefore b=2\times3=6\) (From (1)) Hence, the required number is ab = 36. Correct option is A) 36

The ratio between a two-digit number and the sum of digits of that number is 4 : 1. If the digit in the unit place is 3 more than the digit in the tenth place. What is that number ? A) 36B) 49 C) 86 D) 92

Answer»

Correct option is (A) 36

Let the number be ab or (10a+b).

Given that ratio of two-digit number and the sum of digit of that number is 4 : 1.

\(\therefore\) \(\frac{10a+b}{a+b}=\frac41\)

\(\Rightarrow\) 10a+b = 4a+4b

\(\Rightarrow\) 6a = 3b

\(\Rightarrow\) b = 2a _____________(1)

According to \(2^{nd}\) condition, we have

b = a+3 _____________(2)

\(\Rightarrow\) 2a = a+3 (From (1))

\(\Rightarrow\) a = 3

\(\therefore b=2\times3=6\) (From (1))

Hence, the required number is ab = 36.

Correct option is A) 36