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. the team which lost, scored one-half of their runs in 30 overs and in 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 the last seven overs?
[3 MARKS]

Answer 1

Steps: [2 Marks]
Result: [1 Mark]

Total runs scored by the team that lost = 310 - 10 = 300

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

i.e. in 30 overs, this team scored $=\frac{300}{2}$

=150 runs

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 overs

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