If 3 : x :: x : 48, then the value of x is:

Explanation

The expression 3 : x :: x : 48 says that the two ratios are in proportion. NCERT states that when two ratios are equivalent, the four quantities are in proportion, and that cross products in proportions are equal. Applying that rule here, the product of the extremes equals the product of the means: 3 multiplied by 48 equals x squared. So x^2 = 144. Taking the positive square root gives x = 12. In the middle proportional form a : b :: b : c, the middle term satisfies b^2 = a multiplied by c.

Why the other options are wrong

• (A) 16 is wrong because 16^2 = 256, not 3 x 48 = 144.
• (C) 18 is wrong because 18^2 = 324, so it does not satisfy the cross-product condition for the proportion.
• (D) 24 is wrong because 24^2 = 576, whereas the middle term must square to 144.

Concept

This tests ratio and proportion, especially the cross-product rule and the middle proportional form a : b :: b : c. It recurs in RAS reasoning because it checks whether a candidate can turn a compact analogy-style ratio into a simple equation.

Source

• NCERT Class VII Mathematics Exemplar Problems

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