Question

During a weight-lifting routine, an athlete calculates the total amount of weight moved while performing a certain exercise by multiplying the amount of weight per lift by the number of lifts. On Wednesday, the weight per lift was $20$ percent greater than the weight per lift on Monday, while the number of lifts was $25$ percent less than the number of lifts performed on Monday. On Friday, the weight per lift was $25$ percent greater than the weight per lift on Wednesday, while the number of lifts was $40$ percent less than the number of lifts performed on Wednesday. The total weight moved by the athlete while performing the exercise on Monday was approximately what percent greater than the total weight she moved while performing the exercise on Friday?

• A. $12\%$
• B. $23\%$
• C. $48\%$
• D. $50\%$
• E. $100\%$

Answer 1

The correct option is C $48\%$

$w$ be weight per lift.

$W$ be total lift.

$n$ be the number of lifts.

$W=w\times n$

$w_{wed}=1.2w_{mon}$

$n_{wed}=0.75n_{mon}$

$w_{fri}=1.25w_{wed}$

$w_{fri}=1.25\times 1.2w_{mon}=1.5w_{mon}$

$n_{fri}=0.6n_{wed}$

$n_{fri}=0.6\times 0.75n_{mon}=0.45n_{mon}$

$W_{fri}=n_{fri}\times w_{fri}=0.45\times 1.5w_{mon}=0.675w_{mon}$

$w_{mon}=1.48w_{fri}$

Monday she moved weight $0.48$ more

$\Rightarrow \frac{w_{mon}-w_{fri}}{w_{fri}}\times 100=487$