Exercise_5b_fb

Problems on numbers

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Answer 3 = One number = 33

Another number = 56

Step-by-step explanation:

given that,

wo numbers are in the ratio 4:7

let the common ratio be x

so,

one number will 4x

and another number will 7x

also given that,

4:7. if 4 is subtracted from each of the number,then the ratio becomes 7:13

so,

According to the question

(4x - 4)/(7x - 4) = 7/13

by solving the equation

13(4x - 4) = 7(7x - 4)

52x - 52 = 49x - 28

52x - 49x = -28 + 52

3x = 24

x = 24/3

x = 8

so,

we have the common ratio of the two numbers = 8

given numbers = 4x

= 4(8)

= 32

another number = 7x

= 7(8)

= 56

so,

One number = 33

Another number = 56
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Answer 4 = Let 3x, 5x are number add 5,
3x+5, 5x+5

ratio = 2:3

3x+5/5x+5 = 2/3

= 3(3x+5) = 2(5x+5)

= 9x+15 = 10x-10

= 10x-9x = 15-10

therefore x=5,

3x = 3x5=15

5x= 5x5=25.~~full-width~~
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Problems on Age

Answer 6: let the age of rani be x years
and father's age be (43- x)
six years hence,
rani's age will (x+6)
father's age will ( 43-x+6)
(49-x)
ATQ
(49-x) = 4(x+6)
49-x= 4x + 24
49-24= 4x + x
25 = 5x
x= 5 years
father's age is (43- x)
( 43- 5)
= 38 years
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Answer 7: x= 17, y= 28
Step-by-step explanation:
x = jagruti
y = aunt
(x + 5) = (2/3)(y + 5)
(x - 3) = (1/2)y
put the system of linear equations into standard form
x + 5 = (2/3)y + 10/3
x - 3 = (1/2)y
x - (2/3)y = 10/3 - 15/3
x - (1/2)y = 3
x - (2/3)y = -5/3
x - (1/2)y = 3
3x - 2y = -5
2x - y = 6
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Answer 8 =

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Answer 9 =

Let the age of the A and B five years ago be x and y respectively.

According to the question,

x = 2y - 5 ---------------------------------------eq(i)

Now, present age of A = (x + 5) years.

---------------------- B = (y + 5)years.

After 3 years from present age of A = (x + 5)+ 3 years.

=(x + 8) years.

B = (y +5) +3 years.

= (y + 8) years.

According to the question,

1/3(y + 8) = (x +8) - 12

y + 8 = 3( x + 8 -12)

y + 8 = 3(x - 4))

y + 8 = 3x - 12

3x - y = 12 + 8

3x - y = 20 --------------------------------------------------eq(2)

Putting eq(1) in eq(2),

3(2y - 5) - y = 20

6y - 15 - y = 20

5y = 20 + 15

5y = 35

y = 7 years.

Putting y = 7 in eq(i)

We get,

x = 2(7) - 5

x = 14 - 5

x = 9 years.

Thus, Present age of A = x + 5

= 9 + 5

= 14 years.

B = y + 5

= 7 + 5

= 12 years.

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Problems on two-digit numbers

Answer 11 =

Suppose the number is 10a + b.

The first part of the question says that (10a + b)/(a + b) = 4 or b = 2a.

The second sentence of the question says that (10b+ a) = 2(10a + b) - 6 or 19a -8b = 6.

Substituting b = 2a, 3a = 6 or a = 2. Therefore b = 4 and the number is 24.

CHECK: 24/(2 + 4) = 4 and 42 = 2 x 24 - 6.

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Answer 13 =
Let the original number be 10x + y and the number obtained by reversing the digits be 10y + x, then
10x + y + 10y + x = 154
⇒11x + 11y = 154
⇒x + y = 14 ........(i)
x - y = 2
⇒ x = 2 + y .......(ii)
substituting (ii) in (i), we get
2y + 2 = 14
⇒ y = 6
∴ x = 8
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Answer 15 =
Let the digit at ten be x
unit be y
original number= 10x+y
interchange number = 10y + x
from 1st condition

from 2nd condition
x - y = 1..........2

multiply 2 with -4
-4x + 4y = -4.............3

adding 1 and 3 we get
y=4
put y=4 in 2
x-y=1
x-(4)=1
x=5
therefore original number is 54
and interchange number is 45.
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