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# If $720$ is divided between x and y in the ratio $4:5.$ How many rupees will each get?

Last updated date: 23rd Jul 2024
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Hint: Given that x and y in the ratio $4:5.$ so first of all we will find the total parts of the given number by adding the ratios and then frame the part of “X” in the total and similarly the part of “y” in the total and simplify for the resultant values.

Given that: $720$ is divided between x and y in the ratio $4:5.$
Now, the total parts done from the complete given number is given by $4 + 5 = 9$
Now, the “x” part can be given by $= \dfrac{4}{9} \times 720$
Find the factors for the term in the numerator –
the value of “x” part $= \dfrac{4}{9} \times 80 \times 9$
Common factors from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator.
the value of “x” part $= 4 \times 80$
Simplify finding the product of the terms in the above expression –
The value of “x” part $= 320$ Rs. …… (A)
Similarly, Now, the “y” part can be given by $= \dfrac{5}{9} \times 720$
Find the factors for the term in the numerator –
the value of “y” part $= \dfrac{5}{9} \times 80 \times 9$
Common factors from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator.
the value of “y” part $= 5 \times 80$
Simplify finding the product of the terms in the above expression –
The value of “y” part $= 400$ Rs. …… (B)
Hence, X will receive Rs. $320$ and Y will receive Rs. $400$

Note: Always check the first mathematical expression framed from the given word statements since it is the base of the solution. One can get the amount of Rs. Of others if one is received. For example, if X rupees is got, we can get Y's rupees by subtracting X’s Rs. From the total rupees.