question_answer 15)

                Lakshmi is a cashier in a bank She has currency notes of denominations Rs. 100, Rs. 50 and Rs. 10, respectively. The ratio of the number of these notes is 2 : 3 : 5. The total cash with Lakshmi is Rs. 4,00,000. How many notes of each denomination does she have?

Answer:

                Let the number of currency notes of denominations Rs. 100, Rs. 50 and Rs. 10 be \[2x,\,3x\] and \[5x\] respectively. The amount she has (i) from 100 rupee notes \[=2x\times 100=200x\] (ii) from 50 rupee notes \[=3x\times 50=150x\] (iii) from 10 rupee notes \[=5x\times 10=50x\] Hence, the total money she has \[=200x+150x+50x\] \[=400x\] But the total cash with her is Rs. 4,00,000. Therefore, \[400x=4,00,000\] \[\Rightarrow \]               \[x=\frac{4,00,000}{400}\]                           | Dividing both sides by 400 \[\Rightarrow \]               \[x=1000\] \[2x=2\times 1000=2000\] \[3x=3\times 1000=3000\] and        \[5x=5\times 1000=5000\] Hence, she has 2000, 3000 and 5000 notes of denominations Rs. 100, Rs. 50 and Rs. 10 respectively. Check: 2000 : 3000 : 5000 = 2 : 3 : 5 \[2000\times 100=2,00,000\] \[3000\times 50=1,50,000\]         | as desired \[5000\times 10=50,\,000\] \[2,00,000+1,50,000+50,000=4,00,000\].