Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is

The correct option is 60 (Option 1, corresponding to index 1).

Let the total marks of the examination be $T$.
Initially, Meena's score is 40% of $T$, which is $0.4T$.
After review, her score is increased by 50%, so her post-review score becomes:
$0.4T\times 1.5=0.6T$.
Since she fails by 35 marks with this score, the passing mark is:
$P=0.6T+35$ (Equation 1).

If her post-review score ($0.6T$) is increased by 20%, her new score becomes:
$0.6T\times 1.2=0.7T$.
In this case, she has 7 marks more than the passing score, so the passing mark is:
$P=0.72T-7$ (Equation 2).

Equating the two expressions for the passing mark $P$:
$0.6T+35=0.72T-7$
$35+7=0.72T-0.6T$
$42=0.12T$
$T=\frac{42}{0.12}=350$ marks.

Now we substitute $T=350$ back to find the passing score:
$P=0.6\left(350\right)+35=210+35=245$ marks.

The percentage score needed for passing is:
$\frac{P}{T}\times 100=\frac{245}{350}\times 100=70\%$.

Therefore, the percentage score needed for passing is 70%.