Quantity of acid in the mixture = (2/3) x 60 = 40 L
Quantity of water in the mixture = (1/3) x 60= 20 L
Let the required quantity of water be x L.
According to the question,
40/(20+ x) = 1/2

Correct Option: B

Quantity of acid in the mixture = (2/3) x 60 = 40 L
Quantity of water in the mixture = (1/3) x 60= 20 L
Let the required quantity of water be x L.
According to the question,
40/(20+ x) = 1/2
⇒ 80 = 20 + x
⇒ x = 60 L

Given that
A : B = 3 4 = ( 3 x 2 ) : (4 x 2 ) = 6 : 8
B : C = 8 : 9

Correct Option: D

Given that
A : B = 3 : 4 = ( 3 x 2 ) : (4 x 2 ) = 6 : 8
B : C = 8 : 9
∴ A : B : C = 6 : 8 : 9
As consequent of the first ratio is equal to the antecedent of second ratio.

Required compound ratio = (2 x 5 x 4) / (7 x 3 x 7)

Correct Option: B

Required compound ratio = (2 x 5 x 4) / (7 x 3 x 7)
= 40/147
= 40 : 147

Let the cost of third variety tea will be ₹ N per kg
According to the question,
(126 + 135 + 2N)/4 = 153

Correct Option: C

Let the cost of third variety tea will be ₹ N per kg
According to the question,
(126 + 135 + 2N)/4 = 153
⇒ (261 + 2N) = 4 x 153
⇒ 2N = 612 - 261 = 351
∴ N = 351/2 = 175.50
⇒ N = ₹ 175.5
Hence, the cost of third variety tea is ₹ 175.50 per kg .

(a + b) / (a - b) = 5/3
⇒ 3a + 3b = 5a - 5b
⇒ 2a = 8b
⇒ a = 4b,
⇒ a/b = 4/1

Now, ( a² + b² ) / (a² - b² ) = [a² / (b²+1)] / [a² / (b² -1)]
= [( a/b )² + 1] / [( a/b )² - 1] = [( 4/1 )² + 1] / [( 4/1 )² - 1]
= [16 + 1] / [16 - 1] = 17/15

Correct Option: A

(a + b) / (a - b) = 5/3
⇒ 3a + 3b = 5a - 5b
⇒ 2a = 8b
⇒ a = 4b,
⇒ a/b = 4/1

Now, ( a² + b² ) / (a² - b² ) = [a² / (b²+1)] / [a² / (b² -1)]
= [( a/b )² + 1] / [( a/b )² - 1] = [( 4/1 )² + 1] / [( 4/1 )² - 1]
= [16 + 1] / [16 - 1] = 17/15
∴ ( a² + b² ) : ( a² - b² ) = 17 : 15