Question

A is greater than B by 1/3/4 the sum of A and B. If
B is increased by 40, it becomes greater than twice A
by 10. Find A B
(A) 30, 20(B) 60, 30 (C) 20. 10 (D) 20,40​

Answer 1

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A is greater than B by 1/3rd the sum of A and B.

=> (A - B) = 1/3 (A + B)

=> 3×(A - B) = A + B

=> 3A - 3B = A + B

=> 3A - A - 3B - B = 0

=> 2A - 4B = 0

=> A - 2B = 0 -----------(1)

Now,if B is increased by 40,it becomes greater than twice A by 10.

=> (B+40) - (2A) = 10

=> -2A + B = 10-40

=> -2A + B = -30

=> 2A - B = 30 ---------(2)

Now,lets multiply equation (2) by 2,

4A - 2B = 60 ----------(3)

Now,lets subtract equation (3) by (1),

(A - 2B) - (4A - 2B) = 0-60

=> -3A -60

=> A = 20

Lets put value of A in equation (1),

A - 2B = 0

=> 20 - 2B = 0

=> 2B = 20

=> B = 10

● So the value of A is 20

&

● value of B is 10.

therefore answer is C

●●● Hope It Helps ●●●

Answer 2

A is greater than B by 1/3rd the sum of A and B.

=> (A - B) = 1/3 (A + B)

=> 3×(A - B) = A + B

=> 3A - 3B = A + B

=> 3A - A - 3B - B = 0

=> 2A - 4B = 0

=> A - 2B = 0 -----------(1)

Now,if B is increased by 40,it becomes greater than twice A by 10.

=> (B+40) - (2A) = 10

=> -2A + B = 10-40

=> -2A + B = -30

=> 2A - B = 30 ---------(2)

Now,lets multiply equation (2) by 2,

4A - 2B = 60 ----------(3)

Now,lets subtract equation (3) by (1),

(A - 2B) - (4A - 2B) = 0-60

=> -3A -60

=> A = 20

Lets put value of A in equation (1),

A - 2B = 0

=> 20 - 2B = 0

=> 2B = 20

=> B = 10

● So the value of A is 20

&

● value of B is 10.

therefore answer is C