Question

6. The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of
their
ages
will be 3:4. Find their present ages.
7. The denominator of a rational number is greater than its numerator by 8. If the
numerator is increased by 17 and the denominator is decreased by 1, the number
3
obtained is Find the rational number.
2​

Answer 1

Answer:

6. Answer :-

Let

• Hari's age = 5x
• Harry's age = 7x

After 4 years theirs age will be in the ratio of 3:4

• $\frac{5x~+~4}{7x~+~4}$ = $\frac{3}{4}$

• 4 (5x + 4) = 3 (7x + 4)
• 20x + 16 = 21x + 12
• 20x - 21x = 12 - 16
• -1x = -4
• x = 4

Their present age,

• Hari's age = 5x = 5 × 4 → 20 years
• Harry's age = 7x = 7 × 4 → 28 years

7. Answer :-

Let

• The number = x

so

• the increased number = x + 8
• another increased number = x + 17

→ $\frac{x~+~17}{x~+~8}$ - 1 = $\frac{3}{2}$

→ $\frac{x~+~17}{x~+~7}$ = $\frac{3}{2}$

→ 2 (x + 17) = 3 (x + 7)

→ 2x + 34 = 3x + 21

→ 34 - 21 = 3x - 2x

→ 13 = x

→ x = 13

• The rational number = $\frac{x}{x~+~8}$

• $\frac{13}{13~+~8}$

• $\frac{13}{21}$

Answer 2

Required Solution:

The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.

$\rm \gray { Solution:- }$

As per the given question,we have:

• Ratio of the ages of Hari and Harry is 5:7.
• Four years from now the ratio of their ages will be 3:4

To find:

• Their present ages.

Calculation:

Let their both ages be 5y and 7y.

|| According to the question: ||

$\sf { \longmapsto \dfrac{5y + 4}{7y+4} = \dfrac{3}{4} }$

Now,by cross multiplication:

$\sf { \longmapsto 4(5y+4) = 3(7y+4) }$

$\sf { \longmapsto 20y +16 = 21y +12}$

$\sf { \longmapsto 20y -21y = 12-16}$

$\sf { \longmapsto -y = -4}$

$\sf { \longmapsto y = 4}$

Therefore, there present ages :

• Hair's present age = 5y = 5 × 4 = 20years
• Harry's present age = 7y = 7 × 4 = 28 years

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7. The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

$\rm \gray { Solution:- }$

As per the given question,we have:

• The denominator of a rational number is greater than its numerator by 8.
• If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2

To find:

• The original number.

Calculation:

Let's assume the numerator as y.

• Therefore, denominator becomes = y + 8

The original number $\sf { \longmapsto \dfrac{y }{y+8} }$

|| Now, According to the question: ||

$\sf { \longmapsto \dfrac{y + 17}{y+8-1} = \dfrac{3}{2} }$

$\sf { \longmapsto \dfrac{y + 17}{y+7} = \dfrac{3}{2} }$

Now,by cross multiplication:

$\sf { \longmapsto 2(y+17)= 3(y+7) }$

$\sf { \longmapsto 2y + 34 = 3y + 21 }$

$\sf { \longmapsto 2y -3y = 21 -34 }$

$\sf { \longmapsto -y = -13 }$

$\sf { \longmapsto y = 13 }$

Now,

The original number $\sf { \longmapsto \dfrac{y }{y+8} }$

$\sf { \longmapsto \dfrac{13}{13+8} }$

$\sf \gray { \longmapsto \dfrac{13}{21} }$

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