This question was previously asked in

Official Paper 23: Held on 13th Nov 2020 Shift 1

Option 1 : \(\frac{3}{{17}}\)

**Given**:

20% of (a + b) = 50% of ab ----(i)

40% of (a - b) = 70% of ab ----(ii)

**Calculations**:

What fraction of a is b means b/a

20% = 20/100 ⇒ 1/5

40% = 40/100 ⇒ 2/5

50% = 50/100 ⇒ 1/2

70% = 70/100 ⇒ 7/10

Substitute the values in equation (i) and (ii)

20% of (a + b) = 50% of ab

⇒ (1/5) × (a + b) = (1/2) × ab

⇒ 2 × (a + b) = 5 × ab

⇒ 2a + 2b = 5ab ----(iii)

40% of (a - b) = 70% of ab

(2/5) × (a - b) = (7/10) × ab

4 × (a - b) = 7ab

⇒ 4a - 4b = 7ab ----(iv)

Multiply equation iii with 2

⇒ 2 × ( 2a + 2b) = 5ab × 2

⇒ 4a + 4b = 10ab ----(v)

Add equation iv and v, we get

8a = 17ab

⇒ b = 8/17

Substitute value of b in equation iv

4a - 4 × 8/17 = 7 × a × 8/17

⇒ (68a - 32)/17 = 56a/17

⇒ 68a - 32 = 56a

⇒ 68a - 56a = 32

⇒ 12a = 32

⇒ a = 8/3

Fraction of a is b = (8/17)/(8/3)

⇒ 3/17

**∴ Fraction of a is b = 3/17**

** **20% of (a + b) = 50% of ab

⇒ (20/100) × (a + b) = (50/100) × ab

⇒ (1/5) × (a + b) = (1/2) × ab

⇒ 2 × (a + b) = 5 × ab

⇒ 2a + 2b = 5ab

⇒ (2/5)a + (2/5)b = ab ----(1)

And, 40% of (a - b) = 70% of ab

⇒ (40/100) × (a - b) = (70/100) × ab

(2/5) × (a - b) = (7/10) × ab

4 × (a - b) = 7ab

⇒ 4a - 4b = 7ab

⇒ (4/7)a - (4/7)b = ab ----(2)

Equating (1) and (2) get,

(2/5)a + (2/5)b = (4/7)a - (4/7)b

⇒ (2/5)b + (4/7)b = (4/7)a - (2/5)a

⇒ (34/35)b = (6/35)a

⇒ b = (6/34)a

⇒ b = (3/17)a

**∴ b is (3/17) of a.**