Question

In a match of 50 overs, the team batting second was given a target of 310.They lost the match by 10 runs. The team batting second, i.e. lost team, scored one half of their runs in 30 overs and next five overs they scored one half of the remaining runs. Later in the next 8 overs they scored $\frac{1}{5}$^th of the remaining runs . In last seven overs they scored the remaining runs. How many runs did they score in last seven overs?
[3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Total runs scored by the team that lost = 300

Now, total no. of overs played by them = 50

That is in 30 overs, this team scored $=\frac{300}{2}$

$=150runs$

The balance 300 - 150 = 150 runs were scored by this team in balance 20 overs.

By the given condition

In the next 5 overs $\frac{1}{2}$ of 150 runs

= 75 runs were scored.

$\Rightarrow$ 150 runs - 75 runs = 75 runs are still in balance.

Again in the next 8 overs.

$\frac{1}{5}$ of 75 = 15 runs were scored.

Now No. of overs left = 20 - (5 + 8)

$=20-13$

$=7$

In seven overs, runs scored will be 75 - 15 = 60