Question

5. The two numbers are in the ratio of 1: 2. If both the
numbers are increased by 10, their ratio becomes 2 :
3. Find the numbers.
10 added to thrice a whole number gives 46. find the
number
7 Two numbers differ by 5, If their sum is 19, then
find the two numbers.
8.
Find a number such that when it is added to
two-third of itself, the result is 70.
​

Answer 1

Answer:

5) The numbers are 10 and 20.

3) 12

7) The numbers are 12 and 7.

8) The number is 70.

Step-by-step explanation:

5) Let the common multiple be x,

$\frac{1x + 10}{2x + 10} = \frac{2}{3}$

⇒ 3x + 30 = 4x + 20

⇒ 4x - 3x = 30 - 20

⇒ x = 10

The numbers are,

1x = 1 × 10 = 10

2x = 2 × 10 = 20

6) 10 + 3x = 46

= 3x = 46 - 10

= 3x = 36

= x = 12

7) Let the numbers be x and y,

x + y = 19                                                            -------------- (Equation 1)

x - y = 5                                                              -------------- (Equation 2)

x + y - (x - y) = 19 - 5

x + y - x + y = 14

2y = 14

y = 7

x - y + (x - y) = 19 + 5

x - y + x - y = 24

2x = 24

x = 12

8) Let the number be x,

x + ($\frac{2}{3}$ of x) = 70

x + $\frac{2x}{3}$ = 70

$\frac{5x}{3}$ = 70

3x = 70 × 3

3x = 210

x = 70

Hope It Helps!