If the sum of two numbers is 126 and their HCF and LCM are 7 and 180, respectively, then the sum of the reciprocals of the two numbers is:
- A1
11
- B9
1
- C10
1
- D12
1
Solution & Step-by-step Explanation
Let the two numbers be x and y.
We are given:
Sum of the numbers: x+y=126
HCF=7
LCM=180
We know that the product of two numbers is equal to the product of their HCF and LCM:
x×y=HCF×LCM=7×180=1260
We need to find the sum of the reciprocals of the two numbers:
x
1
+
y
1
=
x×y
x+y
Substituting the known values:
x
1
+
y
1
=
1260
126
=
10
1
We are given:
Sum of the numbers: x+y=126
HCF=7
LCM=180
We know that the product of two numbers is equal to the product of their HCF and LCM:
x×y=HCF×LCM=7×180=1260
We need to find the sum of the reciprocals of the two numbers:
x
1
+
y
1
=
x×y
x+y
Substituting the known values:
x
1
+
y
1
=
1260
126
=
10
1