Question

A jeweler has five gold necklaces P, Q, R, S and Teach having a different weight. (1)P weight twice as much as Q. (2)Q weight four and a half time as much as R. (3)R wait half as much as S. (4)S weight half as much as T. (5)T wait less than P but more than R. Which of the above given statement is not necessary to determine the correct order of necklace according to the​

Answer 1

Given : Five gold necklaces P, Q, R, S and T each having a different weight

Five statements are given

To Find : Which of the given statement is not necessary to determine the correct order of necklace a

Solution:

(1)P weight twice as much as Q.

=> P = 2Q

and P > Q

(2) Q weight four and a half time as much as R.

=> Q = 4.5 R

=> Q > R

(3) R wait half as much as S.

=> R = S/2

=>  S = 2R

S > R

While   S = 2R  and  Q = 4.5 R

Hence       S < Q

=> Q > S

4) S weight half as much as T

S = T/2

=> T = 2S  

T > S

T = 2S   = 2(2R) = 4R

Q = 4.5 R

=> Q > T

Combining all , correct order is

P > Q  > T  >  S  >  R

Hence

(5) T wait less than P but more than R is not required

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Answer 2

Given:

A jeweler has five gold necklaces $P$, $Q$, $R$, $S$, and $T$, each having a different weight.

• Weight of $P$ = $2Q$
• Weight of $Q$ = $4\frac{1}{2}R$
• Weight of $R$ = $\frac{1}{2}S$
• Weight of $S$ = $\frac{1}{2} T$
• Weight of $R$ < Weight of $T$ < Weight of $P$

To Find:

The unnecessary statement in the determination of the correct order of the necklace according to their weights.

Solution:

P weighs twice as much as Q, hence,

• Weight of $P$ = $2Q$
• $P > Q$

Q weighs four and a half times as much as R, hence,

• Weight of $Q$ = $4\frac{1}{2}R$
• $Q > R$

R weighs half as much as S, hence,

• Weight of $R$ = $\frac{1}{2}S$
• $S = 2R$
• $S > R$

Since, $S = 2R$ and $Q$ = $4\frac{1}{2}R$, hence,

• $S < Q$

$S$ weighs half as much as $T$, hence,

• Weight of $S$ = $\frac{1}{2} T$
• $T > S$

Since, $T=2S$

Using the value of $S=2R$ in this equation, we get,

• $T = 4R$

Hence, $Q = 4.5 R$

• ∴ $Q > T$

On combining all the results we get,

$P > Q > T > S > R$

Hence, statement ($5$) $T$ weighs less than $P$ but more than $R$ is not necessary.

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