Question 111

If a - b : b - c : c - d = 1 : 2 : 3, then what is the value of (a + d) : c?

Solution

Given = $$(a-b):(b-c):(c-d)=1:2:3$$

=> $$\frac{a-b}{b-c}=\frac{1}{2}$$

=> $$2a-2b=b-c$$

=> $$2a+c=3b$$ -----------(i)

Similarly, $$\frac{b-c}{c-d}=\frac{2}{3}$$

=> $$3b-3c=2c-2d$$

=> $$3b=5c-2d$$ ----------(ii)

Substituting above value in equation (i), we get :

=> $$2a+c=5c-2d$$

=> $$2a+2d=5c-c$$

=> $$2(a+d)=4c$$

=> $$\frac{a+d}{c}=\frac{4}{2}=2$$

$$\therefore$$ $$(a+d):c=2:1$$

=> Ans - (B)

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