Question

Divide 33,276 ruppees between A, B and C such that their shares are in the ratio of 1/3 : 1/4 : 1/5.

Answer 1

Answer:

Share of A is Rs. 14160, share of B is Rs. 10620 and share of C is Rs. 8496.

Step-by-step explanation:

As per the provided information in the given question, we have :

• Total amount = Rs. 33276
• Total amount has to be divided between A, B and C in the ratio of 1/3 : 1/4 : 1/5.

We are asked to calculate the share of each.

Let us suppose their shares as 1/3x , 1/4x and 1/5x.

According to the question, if the total amount has to be divided in 3 parts, so the sum of the total parts is equivalent to the total amount. Writing it in the form of an equation,

$\longmapsto\rm {Share_{(A)}+Share_{(B)}+ Share_{(C)} = Amount_{(Total)} }$

Substituting the values.

$\longmapsto\rm {\dfrac{1}{3}x + \dfrac{1}{4}x + \dfrac{1}{5}x = 33276 }$

Taking the L.C.M and making the denominator same in L.H.S in order to perform addition.

$\longmapsto\rm {\dfrac{20x + 15x + 12x}{60} = 33276 }$

Performing addition in the numerator of the fraction in L.H.S.

$\longmapsto\rm {\dfrac{47x}{60} = 33276 }$

Transposing 60 from L.H.S to R.H.S.

$\longmapsto\rm {47x = 33276 \times 60 }$

Performing multiplication in R.H.S.

$\longmapsto\rm {47x = 1996560 }$

Now, transposing 47 from L.H.S to R.H.S.

$\longmapsto\rm {x = \cancel{\dfrac{1996560}{47}} }$

Dividing the terms in R.H.S.

$\longmapsto\bf {x = 42480 }$

Now, we have the value of x that is 42480. Substitute the value of x in the expressions of the shares of A, B, c to find their shares.

Share of A :

$\longmapsto \rm { Share_{(A)} = \dfrac{1}{3}x }$

Substitute the value of x.

$\longmapsto \rm { Share_{(A)} = \dfrac{1}{3}(42480) }$

Rearranging the terms.

$\longmapsto \rm { Share_{(A)} = \cancel{\dfrac{42480}{3}} }$

Dividing 42480 by 3.

$\longmapsto \rm { Share_{(A)} = Rs. \; 14160 }$

Share of B :

$\longmapsto \rm { Share_{(B)} = \dfrac{1}{4}x }$

Substitute the value of x.

$\longmapsto \rm { Share_{(B)} = \dfrac{1}{4}(42480) }$

Rearranging the terms.

$\longmapsto \rm { Share_{(B)} = \cancel{\dfrac{42480}{4}} }$

Dividing 42480 by 4.

$\longmapsto \rm { Share_{(B)} = Rs. \; 10620 }$

Share of C :

$\longmapsto \rm { Share_{(C)} = \dfrac{1}{5}x }$

Substitute the value of x.

$\longmapsto \rm { Share_{(C)} = \dfrac{1}{5}(42480) }$

Rearranging the terms.

$\longmapsto \rm { Share_{(C)} = \cancel{\dfrac{42480}{5}} }$

Dividing 42480 by 5.

$\longmapsto \rm { Share_{(C)} = Rs. \; 8496 }$

∴ The share of A is Rs. 14160, share of B is Rs. 10620 and share of C is Rs. 8496.