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Answer:
6) The smaller number= 45, larger number = 62
7)value of greater no. and smaller no. respectively are : 37 and 29
8)The larger number = 19 and Smaller Number = 13
Step-by-step explanation:
6 ) Let the Smaller number= x
Let the larger Number = y
According to the question,
3y - 4x = 6 ..............................(1)
Also, It is given , (x + y) - 6( y - x ) = 5
⇒ x + y -6y + 6x = 5
⇒ - 5y + 7x = 5 ............................(2)
On solving (1) and (2),
⇒( 3y - 4x = 6 ) × 5 ⇒ 15y -20x = 30
(- 5y + 7x = 5 ) × 3 +(-15y+21x = 15)
x = 45
Substituting x = 45 in (1)
⇒ 3y - (4 ×45) = 6
⇒3y -180 = 6
⇒3y = 180+ 6
⇒3y= 186
⇒y = 186/3
⇒y= 62
∴ The smaller number= 45, larger number = 62
7) Let the Smaller number= x
Let the greater Number = y
According to the question,
2y - 45= x
⇒y= (x +45 )/2..............................(1)
Also , 2x - 21 = y .......................(2)
On solving (1) and (2) ,
⇒ (x +45 )/2 = 2x - 21
⇒ x + 45 = 4x - 42
⇒ 45 + 42 = 4x - x
⇒ 87 = 3x ⇒ x = 87/3 = 29
Substituting x = 29 in (1)
⇒y= (x +45 )/2
⇒y = (29 + 45)/2 = 74/2= 37
so, value of greater no. and smaller no. respectively are : 37 and 29
8) Let larger number be x
and smaller number be y
Dividend = divisor × quotient + remainder
3x = 4 × y + 5
3x = 4y +5
3x - 4y= 5 .................(1)
Also, 6y= 4 × x +2
6y = 4x + 2
4x - 6y = -2 ...............(2)
Eliminate y
multiply (1)by 6
Multiply (2) by 4
18x - 24y = 30
16x - 24y = -8
Subtracting the two equations.,
2x = 38 ⇒ x = 38/2 = 19
Substitute x = 19 in (1)
3 × 19 - 4y= 5
⇒57 -4y = 5
⇒57- 5 = 4y
⇒4y= 52
⇒y= 52/4 = 13
∴The larger number = 19
Smaller Number = 13
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