Rs. 600 are divided among A, B, C so that Rs. 40 more than $$\frac{{\text{2}}}{{\text{5}}}$$ of A's share, Rs. 20 more than $$\frac{{\text{2}}}{{\text{7}}}$$ of B's share and Rs. 10 more than $$\frac{{\text{9}}}{{{\text{17}}}}$$ of C's share may all be equal. What is A's share ?
A. Rs. 150
B. Rs. 170
C. Rs. 200
D. Rs. 280
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & = \frac{2}{5}{\text{A}} + 40 = \frac{2}{7}{\text{B}} + 20 \cr & \Rightarrow \frac{2}{7}{\text{B}} = \frac{2}{5}{\text{A}} + 20 \cr & \Rightarrow {\text{B}} = \frac{7}{2}\left( {\frac{2}{5}{\text{A}} + 20} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{7}{5}{\text{A}} + 70} \right) \cr & {\text{And,}} \cr & = \frac{2}{5}{\text{A}} + 40 = \frac{9}{{17}}{\text{C}} + 10 \cr & \Rightarrow \frac{9}{{17}}{\text{C}} = \frac{2}{5}{\text{A}} + 30 \cr & \Rightarrow {\text{C}} = \frac{{17}}{9}\left( {\frac{2}{5}{\text{A}} + 30} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{34}}{{45}}{\text{A}} + \frac{{170}}{3} \cr & = {\text{A}} + {\text{B}} + {\text{C}} = 600 \cr & \Rightarrow {\text{A}} + \left( {\frac{7}{5}{\text{A}} + 70} \right) + \left( {\frac{{34}}{{45}}{\text{A}} + \frac{{170}}{3}} \right) = 600 \cr & \Rightarrow \frac{{142{\text{A}}}}{{45}} = 600 - \frac{{380}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{1420}}{3} \cr & \Rightarrow {\text{A}} = \frac{{1420}}{3} \times \frac{{45}}{{142}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 150 \cr} $$Related Questions on Ratio
If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : c is equal to
A. 2 : 1
B. 14 : 3
C. 7 : 2
D. 1 : 2
If $$\frac{2}{3}$$ of A=75% of B = 0.6 of C, then A : B : C is
A. 2 : 3 : 3
B. 3 : 4 : 5
C. 4 : 5 : 6
D. 9 : 8 : 10
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