There is a precious gem whose cost is directly proportional with the cube of its weight. That gem is broken into three pieces whose weights are in the ratio of 4:5:6. If the gem was broken into three pieces of equal weights, then the merchant would have suffered a further loss of 24000.
Can you calculate the cost price of the unbroken fem?
Let V be the value of a precious gem and the weight be W.
Now if we see the condition in the problem
V ∝ W3
V ∝ kW3 ---- (1) [k = constant of variation]
Since the weights of the three broken pieces of the precious gem are proportional to 4: 5: 6, we can fairly that their weights are 4w, 5w and 6w respectively.
Therefore the weight of the unbroken piece of gem = 4w + 5w + 6w = 15w
v = k ((15w)^3)
v = 3375k (w^3) ---- (2)
k (w^3) = v/3375.
Let, v1, v2 and v3 be the values of the 3 pieces of weights 4w, 5w and 6w respectively.
v1 = 64k (w^3)
v2 = 125k (w^3)
v3 = 216k (w^3)
Thus the total value of the 3 pieces of the gem
= v1 + v2 + v3
= 405k (w^3)
From equation 2
The total value of the 3 pieces = 405*v/3375
Loss = v - (405*v/3375) ---- (3)
In a similar fashion
The second time it breaks in three equal parts i.e. 1:1:1
In this case total value equals = 3*v/27 ---- (4)
Thus loss = v-(3*v/27 ---- (5)
Now according to the question,
(5) - (3) = 24000
(8v/9) - (2970v/3375) = 24000
v = 2,700,000
In a furniture showroom, the cost of five chairs and three tables is Rs. 3110. If the cost of one chair is Rs. 210 less than the cost of one table, can you find out the cost of two tables and two chairs?