The mean and median of a,band care 50 and 35, respectively, where a<b<c. If c-a=55, then: (i) b-a=10??(ii) a+c=115

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Solution

Q.
The mean and median of $a, b a n d c a r e$ 50 and 35, respectively, where $a < b < c .$ $I f c - a = 55, t h e n :$

(i) b - a = 10 (ii) a + c = 115 (iii) a = 20 (iv) b = 35

Choose the correct option from the following:

1 (i) and (iii)

2 (ii) and (iii)

3 (i) and (iv)

4 (ii) and (iv)

Ans.
(4)

$S i n c e a < b < c Median = b \Rightarrow b = 35 Mean = \frac{a + b + c}{3} = 50 \Rightarrow a + b + c = 150 \Rightarrow a + c = 150 - 35 = 115 ∴ (ii) is correct. G i v e n, a + c = 115 c - a = 55 \Rightarrow a = 30 and c = 85 \Rightarrow b - a = 35 - 30 = 5 ∴ Option (d) is correct.$

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