question_answer 16)

                I have a total of Rs. 300 in coins of denomination Rs. 1, Rs. 2 and Rs. 5. The number of Rs2 coins is 3 times the number of Rs. 5 coins. The total number of coins is 160. How many coins of each denomination are with me?

Answer:

                Let the number of Rs. 5 coins be \[x\] Then, the number of Rs. 2 coins \[=3x\] \[\because \] The total number of coins is 160 \[\therefore \] The number of coins of Rs. 1 \[=160\,-(x+3x)\] \[=160-4x\] The amount I have from Rs. 5 coins \[=5\times x=5x\] from Rs. 2 coins \[=2\times 3x=6x\] from Rs. 1 coins \[=(160-4x)\times 1\] \[=160-4x\] \[\because \]     I have a total of Rs. 300 in coins of denomination Rs. 1, Rs. 2 and Rs 5. \[\therefore \]  \[160-4x+5x+6x=300\] \[\Rightarrow \]               \[160+7x=300\] \[\Rightarrow \]               \[7x=300-160\]  | Transposing 160 to RHS \[\Rightarrow \]               \[7x=140\] \[\Rightarrow \]               \[x=\frac{140}{7}=20\]                   | Dividing both sides by 7 \[\Rightarrow \]               \[3x=20\times 3=60\] and        \[160-4x=160-4\times 20\] \[=160-80=80\] Hence, I have 80, 60 and 20 coins of denomination Rs. 1, Rs. 2 and Rs. 5 respectively. Check:  \[60=20\times 3\] \[80+60+20=160\]            | as desired \[80\times 1+60\times 2+20\times 5=80+120+100\] \[=300\]