A, B, C and D purchased a cine-multiplex for Rs. 56 lakhs. The contribution of B, C and D together is 460% that of A, alone. The contribution of A, C and D together is 366.66% that of B’s contribution and the contribution of C is 40% that of A, B and D together. The amount contributed by D is :
(a) 10 lakh
(b) 12 lakh
(c) 16 lakh
(d) 18 lakh
Ans: (d) 18 lakh
Explanation:
A + B + C + D = 56 _____(1)
B + C + D = \displaystyle \frac{23}{5}A ______(2)
A + C + D = \displaystyle \frac{11}{3}B ______(3)
C = \displaystyle \frac{2}{5}(A + B + D)
\Rightarrow A + B + D = \displaystyle \frac{5}{2}C _____(4)
Rough
460\% = \displaystyle \frac{460}{100} = \displaystyle \frac{23}{5}
366.66\% = 300\% + 66.66\%
\qquad\qquad = 3 + \displaystyle \frac{2}{3}
\qquad\qquad = \displaystyle \frac{11}{3}
From (1) & (2) \rightarrow
A + \displaystyle \frac{23}{5}A = 56
\Rightarrow \displaystyle \frac{28}{5}A = 56
\Rightarrow A = 10
From (1) & (3) \rightarrow
B + \displaystyle \frac{11}{3}B = 56
\Rightarrow \displaystyle \frac{14}{3}B = 56
\Rightarrow B = 12
From (1) & (4) \rightarrow
C + \displaystyle \frac{5}{2}C = 56
\Rightarrow \displaystyle \frac{7}{2}C = 56
\Rightarrow C = 16
Now, from (1) \rightarrow
10 + 12 + 16 + D = 56
\Rightarrow D = 18
Aliter (By Ratio Method)
A + B + C + D = 56
A = 5 \qquad B + C + D = 23 \qquad \Rightarrow 28
B = 3 \qquad A + C + D = 11 \qquad \Rightarrow 14
C = 2 \qquad A + B + D = 5 \qquad \; \Rightarrow 7
Using ratio, we have got (A + B + C + D) as 28, 14, 7, but they should be same
LCM ( 28, 14, 7) = 28
So, we have
A = 5 \qquad B + C + D = 23
B = 6 \qquad A + C + D = 22
C = 8 \qquad A + B + D = 20
\therefore D = 28 – (A + B + C)
\qquad= 28 – (5 + 6 + 8)
\qquad= 19
Now, 28 part = 56
\quad\Rightarrow 9 part = 18
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