Question

Parents of a bride go to a jeweler to buy a diamond ring . The jeweler shows them five different rings D,E,F,G and H. Difference in their prices are as under:
(i) Ring D costs twice as much as ring E.
(ii) Ring E costs four and half times as much as ring F.
(iii) Ring F costs half as much as ring G.
(iv) Ring G costs half as much as ring H
(v) Ring H costs less than ring D but more than ring F.
Which of the following represents prices of the rings in ascending order?

• A. E, G, H, D and F
• B. D, E, G, H and F
• C. H, F, G, D and E
• D. F, G, H, E and D

Answer 1

The correct option is D F, G, H, E and D

We have, $D=2E$
$⟹D>E.$
Again, $E=\frac{9}{2}$F
$⟹E>F$.
Also, $F=\frac{1}{2}$G
$⟹$ F < G.
$G=\frac{1}{2}$H
$⟹G<H$.
Clearly, $D>E>F$ ....(i)
and, $F<G<H$ ....(ii)
It is also given that, $F<H<D$ ....(iii)
Now, $E=\frac{9}{2}$F
or, $E=\frac{9}{4}$G
or, $E=\frac{9}{8}$H
$⟹E>H$ ....(iv)
Using (i), (ii), (iii) and (iv), we get
$F<G<H<E<D$.
Hence, option (D) is the correct answer.