Question

Shobha's Mathematics Test had $75$ problems i.e., $10$ arthimetic, $30$ algebra and $35$ geometry problems. Although she answered $70\%$ of the arithmetic, $40\%$ if the algebra and $60\%$ of the geometry problems correctly, she did not pass the test because she got less than $60\%$ of the problems right. How many more questions she would have needed to answer correctly to earn a $60\%$ passing grade?

Answer 1

Total no. of problems is $75$

$70\%$ of $10$ are arithmetic $=\frac{70}{100}\times 10=7$ right

$40\%$ of $30$ are algebra $=\frac{40}{100}\times 30=12$ right

$60\%$ of $35$ are geometry $=\frac{60}{100}\times 35=21$ right

Total of right problems $=7+12+21=40$

$\%$ of right problems $=\frac{40}{75}\times 100=53.3$%

To get $60\%$ she needs $\frac{60}{100}\times 75=45$ right problems

So she needs $45-40=5$ more problems right to get $60\%$.