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The cost of a precious stone varies directly with the cube of its weight. The stone is broken into three pieces, whose weights are in the ratio 4 : 5 : 6. If the stone had been broken into three pieces of equal weights, then there would have been a further loss of र24,000. What is the cost price of the unbroken stone?
a) 250,000
b) 300,000
c) 4,500,000
d) 2,700,000
Read Solution (Total 3)
-
- Let V be the value of a precious stone of weight W.
Then, from the condition of the problem, we have,
V ∝ W3
V ∝ kW3 ……..... (1) [k = constant of variation]
Since the weights of the three broken pieces are proportional to 4 : 5: 6, we assume their weights as 4w, 5w and 6w respectively.
Hence, the weight of the unbroken piece of stone = 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)
Therefore the total value of the 3 pieces
=v1+v2+v3
=405k(w^3)
from eq 2..........
the total value of the 3 pieces= 405*v/3375
loss = v - (405*v/3375)........................(3)
similarly
second time it breaks in three equal parts i.e 1:1:1
in this case total value equals = 3*v/27............(4)
loss = v-(3*v/27...............................(5)
acc to question
eq(5)-eq(3)=24000
(8v/9)-(2970v/3375)=24000
v=2,700,000
- 11 years agoHelpfull: Yes(14) No(1)
- Let V be the value of a precious stone of weight W.
Then, from the condition of the problem, we have,
V ∝ W^3
V ∝ kW^3 ……..... (1) [k = constant of variation]
Since the weights of the three broken pieces are proportional to 4 : 5: 6, we assume their weights as 4w, 5w and 6w respectively.
Hence, the weight of the unbroken piece of stone = 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)
Therefore the total value of the 3 pieces
=v1+v2+v3
=405k(w^3)
from eq 2..........
the total value of the 3 pieces= 405*v/3375
loss = v - (405*v/3375)........................(3)
similarly
second time it breaks in three equal parts i.e 1:1:1
in this case total value equals = 3*v/27............(4)
loss = v-(3*v/27...............................(5)
acc to question
eq(5)-eq(3)=24000
(8v/9)-(2970v/3375)=24000
v=2,700,000 - 11 years agoHelpfull: Yes(5) No(2)
- ans. (d)2700000
- 11 years agoHelpfull: Yes(0) No(3)
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