Question

You can collect rubies and emeralds as many as you. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weight 0.3kg and each emerald weights 0.4kg. Your bag can carry at most 12kg. What you should collect to get the maximum wealth?
A) 20 rubies and 15 emeralds
B) 40 rubies
C) 28 rubies and 94 emeralds
D) None of these

Answer 1

Hint: According to the question given in the question we have to find the maximum wealth should be collected when you can collect rubies and emeralds as many as you. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weight 0.3kg and each emerald weights 0.4kg. Your bag can carry at most 12kg. So, first of all as given limit the bag can contain = 12kg hence, we have to find the cost of 1 kg ruby of cost 4 crore by dividing the cost 4 crore by the weight of ruby which is 0.3kg
Now, same as we have to find the cost of 1 kg ruby of cost 5 crore by dividing the cost 5 crore by the weight of ruby which is 0.4kg
Now, as given that the cost of ruby is more than the cost of emerald so, we should pick more ruby then emerald. So, we can find how much ruby is in 12kg.

Complete step-by-step answer:
Step 1: First of all we have to find the cost of 1kg of ruby by dividing the cost by the given weight where 0.3kg of ruby costs 4crore.
Hence,
Cost of 1kg ruby:
$
   = \dfrac{4}{{0.3}} \\
   = \dfrac{{40}}{3} \\
   = 13.33 \text{crore}
 $
Step 2: Same as the step 1 now we have to find the cost of 1kg emerald by dividing the cost by the given weight where 0.4kg of ruby cost 5crore.
Hence,
Cost of 1kg emerald:
$
   = \dfrac{5}{{0.4}} \\
   = \dfrac{{50}}{4} \\
   = 12.5 \text{crore} \\
 $
Step 3: Now, the cost of ruby is more than the cost of emerald so, we should pick more ruby then emerald. So, we can find how much ruby is in 12kg.
Hence, 12kg contains ruby:
$
   = \dfrac{{120}}{3} \\
   = 40 \text{ruby}
 $
Final solution: Hence, the maximum wealth we should collect is $ = 40 \text{ruby}$ when you can collect rubies and emeralds as much as you. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weight 0.3kg and each emerald weights 0.4kg. Your bag can carry at most 12kg.

Therefore the correct option is B.

Note: To find the maximum wealth it is necessary to find the cost of 1 kg of 1kg ruby by dividing the cost by the given weight where, 0.3kg of ruby cost 4crore and same as the cost of 1kg emerald by dividing the cost by the given weight where, 0.4kg of ruby cost 5crore.
The cost of ruby is more than the cost of emerald so, we should pick more ruby then emerald to find how much ruby is in 12kg.