Question

There are $3$ strings of different length which together is $35$ cm, The smallest is $\frac{2}{3}$ of the middle one which is $\frac{4}{5}$ of the longest string. What is the length of the longest string?

• A. $12$ cm
• B. $22$ cm
• C. $15$ cm
• D. $18$ cm

Answer 1

The correct option is C $15$ cm

$Letthelengthofthe3stringsbex,yandzinascendingorder.x+y+z=35x=\frac{2}{3}\times yy=\frac{4}{5}\times z,x=\frac{2}{3}\times \frac{4}{5}\times z,\frac{4}{5}z+\frac{8}{15}z+z=35,35z=35\times 15,z=15,thelongeststring$