Everyday Math

Ratio, Rate, and Proportion

Ratio, Rate and Proportion: Level 2 Challenges


A king ordered that a golden crown be made for him from 8 kg of gold and 2 kg of silver. The gold smith took away some amount of gold and replaced it by an equal amount of silver and the crown when made, weighed 10 kg. Archimedes knew that under water gold lost 1/20 th of its weight, while silver lost 1/10 th. When the crown was weighed under water, it was 9.25 kg.

How much gold (in kg) was stolen by gold smith?

If it takes 4 minutes to cut a log into 4 pieces, how many minutes will it take to cut a log into 3 pieces?

Assume all cuts are parallel, and cuts are done sequentially (not simultaneously).

Lily, Betty, and Louisa race each other in a 100 meters race.
All of them run at a constant speed throughout the race.
Lily beats Betty by 20 meters.
Betty beats Louisa by 20 meters.

How many meters does Lily beat Louisa by?

Image credit: Flickr US Army (by CC 2.0)

Two runners start together on a quarter-mile track. The faster runner gains a lap after 1010 minutes. If the sum of their rates is 1414 miles per hour, what is the rate of the slower runner in miles per hour?

Express your answer as a decimal.

Image credit: Flickr Elfgoh

The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?


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