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Mathematics

Assertion (A): If 2x = 3y and 4y = 5z, then x : y : z is equal to 15 : 10 : 8.

Reason (R): If x = y and y = z, then we cannot find the ratio x : y : z.

  1. Both A and R are true, and R is the correct explanation of A.

  2. Both A and R are true, but R is not the correct explanation of A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Ratio Proportion

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Answer

Given,

⇒ 2x = 3y

⇒ xy=32\dfrac{x}{y} = \dfrac{3}{2}

⇒ x : y = 3 : 2

⇒ 4y = 5z

⇒ yz=54\dfrac{y}{z} = \dfrac{5}{4}

⇒ y : z = 5 : 4

Since, x : y = 3 : 2 and y : z = 5 : 4. L.C.M of 2 and 5 is 10.

⇒ x : y = 3 : 2 = (3 × 5) : (2 × 5) = 15 : 10

⇒ y : z = 5 : 4 = (5 × 2) : (4 × 2) = 10 : 8

⇒ x : y : z = 15 : 10 : 8.

∴ Assertion (A) is true.

If x = y and y = z, then by the transitive property of equality, it follows that x = y = z.

x : y : z = x : x : x = 1 : 1 : 1.

∴ Reason (R) is false.

Hence, option 3 is the correct option.

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