If a + b + c = 7/12, 3a – 4b + 5c = 3/4 and 7a – 11b – 13c = – 7/12, then what is the value of a + c?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 5/12
a + b + c = 7/12 .....(1)
3a - 4b + 5c = 3/4 .....(2)
7a - 11b - 3c = -7/12 .....(3)
Multiplying eq(1) by 5 and then subtracting eq(2):
⇒ 2a + 9b = 13/6 .....(4)
Multiplying eq(2) by 13 and then adding 5 times eq(3):
⇒ 74a - 107b = 41/6 .....(5)
Multiplying eq(4) by 37 and then subtracting eq(5):
⇒ b = 1/6
Putting the value of b in eq(1)
a + 1/6 + c = 7/12
⇒ a + c = 7/12 - 1/6 = 5/12