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### Question

If the average of p and q is 38, the average of q and r is 56, and of r and p is 72, then what is the value of p?

**A**

54.

**B**

55.

**C**

53.

**D**

56.

**Soln.**

**Ans: a**

We have three equations (p + q)/2 = average of pq, (q + r)/2 = average of qr and (r + p)/2 = average of rp. Adding these three we get p + q + r = (average of pq + average of qr + average of rp) = (38 + 56 + 72) = 166. So p = 166 - (q + r) = 166 - (2 × average of q and r) = 166 - 2 × 56 = 54.