98.The HCF and LCM of two numbers are 12and 72 respectively. If the su

1.	98.The HCF and LCM of two numbers are 12and 72 respectively. If the sum of thesenumbers is 60, then one of the numbers willbe(1) 12(3) 60(2) 24(4) 72
Answer» Given:Let the two numbers be x & y x+y = 60..............(1) H.C.F= 12, L.C.M= 72 H.C.F × L.C.M = PRODUCT OF 2 NUMBERS 12 × 72 = XY 864 = XY X= 864/y..............(2) Put this value of x in eq 1 x+y= 60864/y + y= 60 (864+ y²)/y = 60 864 + y² = 60 y y² -60y +864=0 y² -36y -24y+864=0 y(y-36)-24(y-36)=0 (y-36)(y-24)= 0 y-36= 0 y=36 y-24=0 y=24Put the value of y= 36 x+y=60 x+ 36= 60 x= 60 -36= 24 x= 24 If y= 36, then x= 24 If y=24, then x= 36 Hence, the numbers are 36 & 24

98.The HCF and LCM of two numbers are 12and 72 respectively. If the sum of thesenumbers is 60, then one of the numbers willbe(1) 12(3) 60(2) 24(4) 72

Answer»

Given:Let the two numbers be x & y

x+y = 60..............(1)

H.C.F= 12, L.C.M= 72

H.C.F × L.C.M = PRODUCT OF 2 NUMBERS

12 × 72 = XY

864 = XY

X= 864/y..............(2)

Put this value of x in eq 1

x+y= 60864/y + y= 60

(864+ y²)/y = 60

864 + y² = 60 y

y² -60y +864=0

y² -36y -24y+864=0

y(y-36)-24(y-36)=0

(y-36)(y-24)= 0

y-36= 0

y=36

y-24=0

y=24Put the value of y= 36

x+y=60

x+ 36= 60

x= 60 -36= 24

x= 24

If y= 36, then x= 24

If y=24, then x= 36

Hence, the numbers are 36 & 24