GATE Overflow Test Series | Quantitative Aptitude | Test 1 | Question: 25

Question

Given that $a:b = 1:3,b:c = 6:20, c:d = 5:2, d:e = 4:5$, the value of $\dfrac{ed + bc}{cd + ab} = $ ________

• A. $\dfrac{43}{43}$
• B. $\dfrac{50}{43}$
• C. $\dfrac{51}{44}$
• D. $\dfrac{50}{41}$

Answer 1

Given that,

• $a:b = 1:3\qquad \rightarrow(1)$
• $b:c = 6: 20 \qquad \rightarrow(2)$ 
• $c:d = 5:2\qquad \rightarrow(3)$
• $d:e = 4:5\qquad \rightarrow (4)$

From equations $(1),(2)$ we get

• $a:b:c = 1:3:10 \qquad \rightarrow (5)$

From equations $(5),(3),(4)$ we get

• $a:b:c:d:e = 1:3:10:4:5\qquad \rightarrow (6)$

Taking the proportionality constant as $k,$ we get $a = k,b = 3k,c = 10k,d = 4k,e = 5k$
     
$\therefore \dfrac{ed + bc}{cd + ab} = \dfrac{20k^{2} + 30k^{2}}{40k^{2} + 3k^{2}} = \dfrac{50k^{2}}{43k^{2}} = \dfrac{50}{43}.$

So, the correct answer is $(B).$