Question

The total salary drawn by 3 watchmen, A, B and C is Rs. 1720. They spend 70 %, 60 % and 50 % respectively from their salaries. If the balance with them is into ratio 1:2:3, what is the salary of each?
A.A Rs. 300, B Rs. 500, C Rs. 700
B.A Rs. 200, B Rs. 300, C Rs. 650
C. A Rs. 100, B Rs. 300, C Rs. 600
D.A Rs. 400, B Rs. 600, C Rs. 720

Answer 1

Hint: We are given the total salary of 3 watchmen A, B and C which is Rs. 1720. Their monthly expenditures are also given from their salaries, so, we will calculate the savings from their expenditures and then we will find their ratio. After that, we will compare this ratio with that of the original ratio to calculate the total ratio of their earnings. Once, we calculated the ratio of their salaries, we can easily find their individual salaries by multiplying the respective ratio with the total salary divided by the total of the ratios.

Complete step-by-step answer:
We are given that the total earnings of 3 watchmen A, B and C is Rs. 1720.
Their individual expenditures are also given as 70 %, 60 % and 50 % respectively.
So, we can say that the balances left with each watchman are 30 %, 40 % and 50 % respectively (since total salary = expenditure + saving).
Therefore, the ratio of their expenditures can be written as: 3:4:5
But we are given the actual ratio of their respective balances, which is: 1:2:3
 Now we can calculate the ratio of their total individual salaries by writing the given ratios in the pattern (pairs) given below:
A B B C
1 2 2 3
3 4 4 5
On cross multiplying, we get
$\left( {1 \times 4} \right):\left( {2 \times 3} \right)$ $\left( {2 \times 5} \right):\left( {3 \times 4} \right)$
$ \Rightarrow $ 4 : 6 10 : 12
Or, 2 : 3 or, 5 : 6
Now, considering B as common, we get the ratio of individual total salary as $\left( {2 \times 5} \right):\left( {3 \times 5} \right):\left( {6 \times 3} \right)$or we can write 10:15:18.
Now, we can calculate the individual salaries of watchman A, B and C by the formula
Individual total salary = individual ratio of total salary$ \times $total amount of salary divided by the sum of the individual ratios of total salary
$ \Rightarrow $salary of watchman A = $\dfrac{{10 \times 1720}}{{43}} = \dfrac{{17200}}{{43}} = 400$
Therefore, the salary of watchman A is Rs. 400.
Similarly, the salary of watchman B = $\dfrac{{15 \times 1720}}{{43}} = \dfrac{{25800}}{{43}} = 600$
Therefore, the salary of watchman B is Rs. 600.
And salary of watchman C = $\dfrac{{18 \times 1720}}{{43}} = \dfrac{{30960}}{{43}} = 720$
Therefore, the salary of watchman C is Rs. 720.
Hence, option(D) is correct.

Note: In such problems, you can face difficulties in determining the formula to be used. Also, you can face difficulties in proceeding after calculating the ratio of their individual savings/balance. You can also solve this problem by the method of direct variation.