Q.42 The figure below shows the rectangle ABCD (not drawn to scale) R is thrice the size of p and 1/2 the size of s. Q is twice the size of p . what fraction of the whole figure is the sum of Q and S ? (a) 1/3 (b) 2/3 (c) 4/5 (d) 6/5     

Dear Student,

Please find below the solution to the asked query:

Given : R is thrice the size of P , So

R =  3 P                                            --- ( 1 )

And R is $\frac{1}{2}$  the size of S , So

R =  $\frac{1}{2}$ S , Now we  substitute value from equation 1 we get : 

3 P = $\frac{1}{2}$ S , 

S = 6 P                                            --- ( 2 )

And  Q is twice the size of P , So 

Q = 2 P                                            --- ( 3 )

Then,


Fraction of the whole figure is the sum of Q and S = $\frac{\mathrm{Q} +\hspace{0.17em}\mathrm{S}}{\mathrm{P} +\hspace{0.17em}\mathrm{Q} + \mathrm{R} + \mathrm{S}} = \frac{{\displaystyle 2 \mathrm{P} + 6 \mathrm{P}}}{{\displaystyle \hspace{0.17em}\mathrm{P} +\hspace{0.17em}2 \mathrm{P} + 3 \mathrm{P} + 6 \mathrm{P}}} = \frac{{\displaystyle 8 \mathrm{P}}}{{\displaystyle 12 \mathrm{P}}} = \frac{\mathbf{2}}{\mathbf{3}}$

Therefore,

Option ( B )                                             ( Ans )


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