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### Question

In a sample there are 450 items having a value of 50°C. 50% values are below 50°C, and the number of values above 50°C is $2/3$ of the items having a value of 50°C. What is the size of the sample?

**A**

1500 items.

**B**

1510 items.

**C**

1490 items.

**D**

1520 items.

**Soln.**

**Ans: a**

The %age ≥ 50°C = (100 - 50) = 50. If x is the size of the sample, 50% of x = 450 + $2/3 × 450$ = ${5 × 450}/3$, which is same as ${50 × x}/100$ = ${5 × 450}/3$. Solving, we get x = 1500.