Question

If a + 2a + 3a + .... + 1000a = 2b + 4b + 6b + .... + 2000b = 3c + 6c + 9c + .... + 3000c
then a : b : c is as
(A) 1 : 2 : 3 (B) 3 : 2 : 1 (C) 2 : 3 : 6 (D) 6 : 3 : 2

Answer 1

The correct answer of your question will be

Option d) 6:3:2 .

a( 1+2+3+....+1000) = 2b (1+2+3+...1000)

=3c (1+2+3+...+1000)

a=2b=3c

Hence a:b:c= 6:3:2

Answer 2

The correct option is (D) 6 : 3 : 2

Given : a + 2a + 3a + .... + 1000a = 2b + 4b + 6b + .... + 2000b = 3c + 6c + 9c + .... + 3000c

To find : The correct option

a : b : c is as

(A) 1 : 2 : 3

(B) 3 : 2 : 1

(C) 2 : 3 : 6

(D) 6 : 3 : 2

Solution :

Step 1 of 4 :

Write down the given expression

The given expression is

a + 2a + 3a + .... + 1000a = 2b + 4b + 6b + .... + 2000b = 3c + 6c + 9c + .... + 3000c

Step 2 of 4 :

Find the relation between a , b , c

⇒ a(1 + 2 + 3 + . . . + 1000) = 2b(1 + 2 + 3 + . . . + 1000) = 3c(1 + 2 + 3 + . . . + 1000)

⇒ a = 2b = 3c

Step 3 of 4 :

Find the ratio

a = 2b = 3c

$\displaystyle \sf{ \implies b = \frac{3c}{2} }$

So the ratio

= a : b : c

$\displaystyle \sf{ = 3c : \frac{3c}{2} : c}$

$\displaystyle \sf{ = 6 : 3 : 2}$

Step 4 of 4 :

Find the correct option

The correct option is (D) 6 : 3 : 2

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