Question

a. Two numbers are in the ratio 11:15. If the difference of the numbers is 32, find the two
numbers.
b. Calculate the area of a circle whose diameter us 1.4 m.
​

Answer 1

$\large{\mathtt{\underbrace{\red{✠\:Required\:Answer\:✠}}}}$

✯ Question 1 :

Two numbers are in the ratio 11:15. If the difference of the numbers is 32, find the two

numbers.

✯ Solution 1 :

Let the numbers be '11x' and '15x'

Their difference = 32

A.T.Q.

15x - 11x = 32

4x = 32

x = $\frac{32}{4}$

x = $\frac{\cancel{32}}{\cancel{4}}$

=> x = 8

Value of numbers :-

11x = 11 × 8 = 88

15x = 15 × 8 = 120

✯ Question 2 :

Calculate the area of a circle whose diameter us 1.4 m.

✯ Solution 2 :

Diameter = 14m

Radius = $\frac{D}{2} = \frac{14}{2} = 7m$

$\huge{\boxed{\mathtt{\color{aqua}{Area\:=\:πr²}}}}$

Where,

• π = $\frac{22}{7}$
• R = Radius

Substituting the value, we get :-

Area = $\frac{22}{7} \times 7 \times 7$

Area = 22 × 7

$\huge{\fcolorbox{blue}{aqua}{Area\:=\:154m²}}$

Answer 2

$\large{\underline{\underline{\sf{\green{Required \; Solution:}}}}}$

1st question:

$\implies \sf{Let \; 1st \; number \; be \; 11x.}$

$\implies \sf{Let \; 2nd \; number\; be \;15x.}$

Now,

              $\longmapsto \tt{11x - 15x = 32}$

              $\longmapsto \tt{4x = 32}$

              $\longmapsto \tt{ x= }\tt{ \dfrac{\cancel {32}}{\cancel 4} =8}$

$\tt{1^{st}\;number=11x=11\times8=\underline{88}}$

$\tt{2^{nd}\;number=15x=15\times8=\underline{120}}$

             $\boxed{\color {brown}{\sf Required\:numbers \begin{cases} \tt{88} \\ \tt 120 \end {cases}}}$

2nd question:

$\implies \sf{Diameter = 1.4}$

$\implies \sf{radius =\dfrac{d}{2} = \dfrac{1.4}{2} = 0.7 m}$

$\sf{Area \; of \; Circle}$  $\longmapsto \tt{ \pi\; r^2}$

                      $\longmapsto \tt{ \dfrac{22}{7} \times 0.7 \times 0.7}$

                      $\longmapsto \tt \dfrac{ 22}{7} \times 0.49$

$~~~~~~~~~~~ \boxed{\sf{\pink{Area= 1.54 \; m^2}}}$

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Hope it helps! :)