Question

The ratio salaries of Ram to Shyam is \[5:6\], and that of their expenditure is \[7:9\], Their savings are Rs. \[4000\] and Rs. \[3000\] respectively, Estimate their salaries.

Answer 1

Hint: We are given a ratio of salaries of Ram to Shyam as \[5:6\], and their expenditure \[7:9\]. First we need to assume the cancelled term in salary ratio as x and y in expenditure. Thereby we would get two simultaneous linear equations which we would solve to get x and y, from where we find the sum of their salaries.

Complete step-by-step answer:
We know that fractions represent equal parts of a whole or a collection. When we divide a whole into equal parts, each part is a fraction of the whole. Likewise if assume the cancelled part in salaries is Rs. x and in expenditure is Rs. y,
\[{{S}_{R}}=5x,{{S}_{S}}=6x\]
Where \[{{S}_{R}}\] refers to the salary of Ram
\[{{E}_{R}}=7x,{{E}_{S}}=9x\]
Where \[{{S}_{S}}\] refers to the salary of Shyam
If we subtract expenditure the savings remain likewise we form two equations –
\[5x-7y=4000\ldots \ldots eq(1)\]
\[6x-9y=3000\ldots \ldots eq(1)\]
We multiply eq(1) by 6 and eq(2) by 5
\[30x-42y=24000\ldots \ldots eq(3)\]
\[30x-45y=15000\ldots \ldots eq(4)\]
We subtract eq(4) from eq(3),
\[3y=9000\]
\[y=3000\] in rupees
We substitute value in y in eq(3)
\[x=5000\] in rupees
From this result we find the salary –
\[{{S}_{R}}=25000\] in rupees
\[{{S}_{S}}=30000\] in rupees
Hence the Salaries of Ram and Shyam is Rs. 25000 and Rs. 30000 respectively.

Note: The student must be aware of the elimination method of solving (mentioned above) a pair of simultaneous linear equations. The common mistake committed by students include multiplication of the equation by wrong factor, not changing the value of constant accordingly on the right side of equations, forgetting to multiply the value of x by given factors of Ram and Shyam’s income in order to find their respective salaries.