যদি x/y = 2/3, y/z = 4/5 হয়, তাহলে (x + y)/(y + z) = ?

প্রশ্ন: যদি x/y = 2/3, y/z = 4/5 হয়, তাহলে (x + y)/(y + z) = ?

সমাধান: 
x/y = 2/3
∴ x = (2y)/3

y/z = 4/5
∴ z = (5y)/4

 (x + y)/(y + z)
= {(2y)/3 + y}/{y + (5y)/4}
= {y (2/3 + 1)}/{y(1 + 5/4)}
= (2/3 +1)/(1 + 5/4)
= (5/3)/(9/4)
= (5 × 4)/(3 × 9)
= 20/27