A number is divided into two parts such that 50% of the first part is 4 more than 40% of the second part, and 70% of the first part is 2 more than 60% of the second part. What is the number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 170
Each statement gives one equation in the two parts; solving them gives both parts, and the number is their sum.
Let the parts be \(a\) and \(b\)
\(0.5a=0.4b+4\), so \(a=0.8b+8\)
\(0.7a=0.6b+2\); putting in \(a=0.8b+8\): \(0.56b+5.6=0.6b+2\)
\(0.04b=3.6\), so \(b=90\) and \(a=0.8\times90+8=80\)
Number \(=80+90=170\)
The number is 170.