Dividing A Quantity In A Given Ratio
If a number n is divided into two parts in the ratio a : b
a
1st Part would be = ------------ X n
a + b
b
2nd Part would be = ----------- X n
a + b
If a number n is divided into three parts in the continued ratio a : b : c,
a
1st Part would be = ------------- X n
a + b + c
b
2nd Part would be = ------------- X n
a + b + c
c
3rd Part would be = ------------- X n
a + b + c
There are some examples are given below for your understanding –
Example.1) If 3a = 4b = 5c, then find a : b : c = ?
Ans.) As per the given condition we have 3a = 4b = 5c
Let, 3a = 4b = 5c = k ( k ≠ 0 )
So, a = k / 3 , b = k / 4, c = k / 5
k k k
So, a : b : c = -------- : --------- : ---------
3 4 5
1 1 1
= --------- : --------- : ---------
3 4 5
( Now, we will find the LCM of denominators of obtained fraction and we find LCM of 3, 4, 5 = 60 )
Now we will multiply by obtained LCM 60 with
1 1 1
-------, --------, -------- and we find -
3 4 5
1 1 1
= ( ------- X 60 ) : ( ------- X 60 ) : ( ------- X 60 )
3 4 5
= ( 1 X 20 ) : ( 1 X 15 ) : ( 1 X 12 )
= 20 : 15 : 12
So, a : b : c = 20 : 15 : 12 (Ans.)
Example.2) Mr. Richard divided his retirement benefit worth $ 2,16,800 to his Son, Daughter & Wife in
2 1 3
the ratio 1 -------- : 2 -------- : 1 --------.
5 3 7
Find how much money Richard’s each family member will get ?
Ans.) As per the given condition, Mr. Richard has distributed his money worth $ 2,16,800 to his three family members
2 1 3
in the ratio of = 1 -------- : 2 -------- : 1 --------
5 3 7
First of all, we have to simplify the given ratio –
2 1 3
1 --------- : 2 --------- : 1 ----------
5 3 7
7 7 10
= --------- : --------- : ----------
5 3 7
Now, we have to find out LCM of the denominator of the obtained fraction is 105, now we multiply each ratio by 105 and we will get –
7 7 10
= ( ------- X 105 ) : ( ------- X 105 ) : ( ------- X 105 )
5 3 7
= ( 7 X 21 ) : ( 7 X 35 ) : ( 10 X 15 )
= 147 : 245 : 150
Now we will find the money distributed to his family members in the ratio of 147 : 245 : 150
147
Son will get = $ 2,16,800 X ---------------------
( 147 + 245 + 150 )
147
= $ 2,16,800 X ------------
542
= 400 X 147 = $ 58, 800
245
Daughter will get = $ 2,16,800 X ----------------------
( 147 + 245 + 150 )
245
= $ 2,16,800 X -------------
542
= 400 X 245 = $ 98,000
150
Wife will get = $ 2,16,800 X -----------------------
( 147 + 245 + 150 )
150
= $ 2,16,800 X --------------
542
= 400 X 150 = $ 60,000
So, Richard’s money will be distributed to his son, daughter & wife by $ 58,800, $ 98,000 and $ 60,000 respectively. (Ans.)
Example.3) A certain quantity of burger is put into two boxes in the ratio 5 : 3, if the bigger box contains 80 pcs of burger then what is the quantity of total burger ?
Ans.) Let the burger in the smaller box be Y pcs.
Then, 80 pcs : Y pcs = 5 : 3
80 5
So, ---------- = ----------
Y 3
So, 5 Y = 80 X 3
80 X 3
So, Y = ------------- = 16 X 3 = 48 pcs
5
So, the total pieces of burger is = 80 + 48 = 128 pieces (Ans.)
Example.4) Three friends x, y & z share $ 780 in such that ratio x : y = 3 : 1 & y : z = 3 : 1, then find the each share of distributed money.
Ans.) As per the given condition given ratio are x : y = 3 : 1 & y : z = 3 : 1
Here we can observe that, consequent of 1st ratio is y = 1 but in the second ratio antecedent y = 3.
So, 3 ÷ 1 = 3
So, now we will multiply 1st ratio by 3 and find -
x : y = 3 : 1 = ( 3 X 3 ) : ( 1 X 3 ) = 9 : 3
Now we have, x : y = 9 : 3 & y : z = 3 : 1
So, now we can find x : y : z = 9 : 3 : 1
9
So, friend x will get the money = $ 780 X ---------------
( 9 + 3 + 1 )
9= $ 780 X --------- = $ 60 X 9 = $ 540
13
3
So, friend y will get the money = $ 780 X --------------
( 9 + 3 + 1 )
3
= $ 780 X -------- = $ 60 X 3 = $ 180
13
1
So, friend z will get the money = $ 780 X -------------- ( 9 + 3 + 1 )
1
= $ 780 X -------- = $ 60 X 1 = $ 60
13
So, distributed money to x, y, & z is $ 540, $ 180, & $ 60 respectively (Ans.)