If on dividing 26 into two parts, we find that three times the first and seven times the second part together equals to 122. Then, the ratio of first and second part shall be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 15:11
The two conditions give two equations in the two parts \(a\) and \(b\); removing one unknown gives the other.
The two conditions (the parts are \(a\) and \(b\)):
The two parts add up to 26: \(a+b=26\) (1)
Three times the first plus seven times the second is 122: \(3a+7b=122\) (2)
Removing \(a\) (making the \(a\) terms equal):
Multiplying (1) by 3: \(3a+3b=78\) (3)
Subtracting (3) from (2), the \(a\) terms cancel: \(4b=44\)
\(b=11\)
The other part (putting \(b=11\) in (1)):
\(a=26-11=15\)
Ratio of the first part to the second: 15:11