Vikram has scored 68, 74, 81 and 77 in four unit tests. What must he score in the fifth test to bring his mean over the five tests up to 78?

Five tests with mean 78 need a total of $5\times 78=390$. The four tests so far add to 68 + 74 + 81 + 77 = 300, so the fifth must be 390 − 300 = 90. Scoring the target 78 itself would leave the mean at 378 ÷ 5 = 75.6, because his present mean is 300 ÷ 4 = 75 and the last test has to lift the earlier four as well as carry its own share: $78+4\times 3=90$. Scores of 82 and 88 fall short, leaving means of 76.4 and 77.6.