Question

3 Sum of three numbers which are in the ratio 3:4:5 is 60. What is the sum of
their squares?
(A)1970
(B)1430
(C)1250
(D)1760​

Answer 1

Answer:

Given :-

• Sum of three numbers are in the ratio of 3 : 4 : 5 is 60.

To Find :-

• What is the sum of their squares.

Solution :-

Let,

$\mapsto$ First number = 3x

$\mapsto$ Second number = 4x

$\mapsto$ Third number = 5x

According to the question,

$\implies \sf 3x + 4x + 5x =\: 60$

$\implies \sf 7x + 5x =\: 60$

$\implies \sf 12x =\: 60$

$\implies \sf x =\: \dfrac{\cancel{60}}{\cancel{12}}$

$\implies \sf x =\: \dfrac{5}{1}$

$\implies \sf\bold{\green{x =\: 5}}$

Hence, the required numbers are :

$\dashrightarrow$ First number :

$\leadsto \sf 3x$

$\leadsto \sf 3(5)$

$\leadsto \sf 3 \times 5$

$\leadsto\sf\bold{\purple{15}}$

$\dashrightarrow$ Second number :

$\leadsto \sf 4x$

$\leadsto \sf 4(5)$

$\leadsto \sf 4 \times 5$

$\leadsto \sf\bold{\purple{20}}$

$\dashrightarrow$ Third number :

$\leadsto \sf 5x$

$\leadsto \sf 5(5)$

$\leadsto \sf 5 \times 5$

$\leadsto \sf\bold{\purple{25}}$

Hence, the three numbers are 15, 20 and 25 respectively.

Now, we have to find their squares :

$\bigstar \sf {(15)}^{2} =\: 15 \times 15 =\: \bold{\purple{225}}$

$\bigstar \sf {(20)}^{2} =\: 20 \times 20 =\: \bold{\purple{400}}$

$\bigstar \sf {(25)}^{2} =\: 25 \times 25 =\: \bold{\purple{625}}$

Hence, their squares are 225, 400 and 625 respectively.

Now, we have to find the sum of their squares :

$\Rightarrow \sf Sum\: of\: their\: squares =\: 225 + 400 + 625$

$\Rightarrow \sf Sum\: of\: their\: squares=\: 625 + 625$

$\Rightarrow \sf\bold{\red{Sum\: of\: their\: squares =\: 1250}}$

$\therefore$ The sum of their squares is 1250 .

Hence, the correct options is option no (c) 1250 .

$\rule{150}{2}$

VERIFICATION :

$\implies \sf 3x + 4x + 5x =\: 60$

By putting x = 5 we get,

$\implies \sf 3(5) + 4(5) + 5(5) =\: 60$

$\implies \sf 15 + 20 + 25 =\: 60$

$\implies \sf\bold{60 =\: 60}$

Hence, Verified.

Answer 2

Let the three numbers of 3x, 4x, and 5x, Sum of the squares of these = 1250.

A/q,

$= (3x) {}^{2} + (4x) {}^{2} + (5x) {}^{2} = 1250$

$= > 9x { }^{2} +16x {}^{2} + 25x {}^{2} = 1250$

$= > 50x {}^{2} = 1250$

$= >x {}^{2} = 1250 \div 50$

$= >x {}^{2} = 25$

$= > x = 5$

Therefore, three numbers are:-

$= > 3x = 3(5) = 15$

$= > 4x = 4(5) = 20$

$= > 5x = 5(5) = 25$

Now,

Sum of these number = 15 + 20 + 25 = 60

Required Answer = 60.

Step-by-step explanation:

@Genius