Question

If 25^{(3a - 2b)} = 5^{(b - a)} = 5² and \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{35}\), then find the value of ab - c.

• A. 1
• B. 0
• C. -1
• D. -2

Answer 1

The Correct Option is B

25^(3a-2b) = 5^(b-a) = 5²
5^2(3a-2b) = 5^b-a = 5²
5^6a-4b = 5^b-a = 5²
5^6a-4b = 5²
6a - 4b = 2
3a - 2b = 1 ....... (1)
5^b-a = 5²
b - a = 2
2b - 2a = 4 ...... (2)
From (1) and (2) :
3a - 2a - 4 = 1
a = 5
b = 7
Now,
\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{35}\)
\(\frac{1}{5}+\frac{1}{7}+\frac{1}{c}=\frac{13}{35}\)
\(\frac{1}{c}=\frac{13}{35}-\frac{1}{5}-\frac{1}{7}=\frac{13-7-5}{35}\)
c = 35
Value of ab - c
= 5 * 7 - 35
= 35 - 35
= 0
So, the correct option is (B) : 0.