Question

Two numbers X and Y are given as:

X = 30% of A + 25% of B

Y = 35% of A + 43% of B

If X is 66.67% of Y, then find out how much percent is A less than B.

1. 45%
2. 12.5%
3. 37.5%
4. 30%

Answer 1

Correct Answer - Option 1 : 45%

Given:

X = 30% of A + 25% of B

Y = 35% of A + 43% of B

X = 66.67% of Y

Formula Used:

If a < b, the

Percentage a less than b = (b - a)/b × 100

Calculations:

X = 66.67% of Y

⇒ X = (2/3) × Y      [66.67% = 2/3]

X = 30% of A + 25% of B

Y = 35% of A + 43% of B

Now, dividing these 2 relations, we get

X/Y = (30% of A + 25% of B)/(35% of A + 43% of B)

⇒ 2/3 = (30A + 25B)/(35A + 43B)

⇒ 2 × ((35A + 43B) = 3 × (30A + 25B)

⇒ 70A + 86B = 90A + 75B

⇒ (90 - 70)A = (86 - 75)B

⇒ 20A = 11B

⇒ A : B = 11 : 20

Required percentage = (20 - 11)/20 × 100

⇒ Required percentage = 45%

∴ The percentage by which A is less than B is 45%.