search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
0 votes
145 views
The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weight in the ratio $1: 2 : 3: 4.$ When the pieces were sold, the merchant got $\text{Rs. 70,000}$ less. Find the original price of the diamond _____________
in Quantitative Aptitude 13.3k points 306 2250 2467
edited by
145 views

1 Answer

0 votes

Given that, the ratio of weights of four pieces $ = \text{P}_{1} : \text{P}_{2} : \text{P}_{3} : \text{P}_{4} : = 1:2:3:4 $

so weights are : 

  • $\text{P}_{1} = k$
  • $\text{P}_{2} = 2k$
  • $\text{P}_{3} = 3k$
  • $\text{P}_{4} = 4k$

The cost of a diamond varies directly as the square of its weight.

So costs are :

  • $\text{P}_{1} = k^{2}$
  • $\text{P}_{2} = (2k)^{2} = 4k^{2}$
  • $\text{P}_{3} = (3k)^{2} = 9k^{2}$
  • $\text{P}_{4} = (4k)^{2} = 16k^{2}$

The weight of original diamond $ = k+2k+3k+4k = 10k$

The cost of original diamond $ =  (10k)^{2} = 100k^{2}$

Now, $100k^{2} – (k^{2} + 4k^{2} + 9k^{2} + 16k^{2}) = 70000 $

$\Rightarrow 100k^{2} – 30k^{2} = 70000$

$\Rightarrow 70k^{2} = 70000$

$\Rightarrow \boxed{k^{2} = 1000}$

$\therefore$ The price of original diamond $ = 100k^{2} = 100 \times 1000$

Correct Answer $:100000  = ₹  100000$

10.1k points 4 8 30

Related questions

0 votes
1 answer
1
136 views
$\frac{2}{5}$ of the voters promise to vote for $\text{P}$ and the rest promised to vote for $\text{Q}$. Of these, on the last day $15\%$ of the voters went back of their promise to vote for $\text{P}$ and $25\%$ of voters went back of their promise to vote for $\text{Q}$, and $\text{P}$ lost by $2$ votes. Then the total number of voters is _________
asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 306 2250 2467 136 views
1 vote
1 answer
2
1.9k views
For all non-negative integers $x$ and $y$, $f(x,y)$ is defined as below. $f( 0,y) = y+1$ $f(x+1,0) = f( x, 1)$ $f( x+1, y+1) = f\left( x,f( x+1,y) \right)$ Then what is the value of $f(1,2)$ ________
asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 306 2250 2467 1.9k views
0 votes
0 answers
3
101 views
A water tank has three taps $\text{A, B},$ and $\text{C. A}$ fills four buckets in $24$ mins, $\text{B}$ fills $8$ buckets in $1$ hour and $\text{C}$ fills $2$ buckets in $20$ minutes. If all taps are opened together a full tank is emptied in $2$ hours. If a buckets can hold $5$ litres of water, what is the capacity of the tank in litres _________
asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 306 2250 2467 101 views
0 votes
1 answer
4
155 views
Let $u_{n+1}=2u_{n}+1 \;(n=0,1,2,\dots)$ and $u_{n}=0$. Then $u_{10}$ nearest to ________
asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 306 2250 2467 155 views
0 votes
1 answer
5
132 views
When you reverse the digits of the number $13$, the number increases by $18$. How many other two digit numbers increase by $18$ when their digits reversed ___________
asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 306 2250 2467 132 views
...