Question

Two numbers are in the ratio 10:11. Their sum is 10. Find the numbers

Answer 1

Answer:

100/21 , 110/21

Step-by-step explanation:

Number A : Number B = 10:11

Number A = 10x

Number B = 11x

Sum of the two numbers = 10

10x + 11x = 10

21x = 10

x = 10/21

Number A = 10x = 10*10/21

= 100/21

Number B = 10/21 * 11

= 110/21

Answer 2

GIVEN :–

▪︎ Ratio of two numbers = 10 : 11

▪︎ Sum of those numbers = 10

TO FIND :–

▪︎ Numbers = ?

SOLUTION :–

• Let the two numbers are 'x' & 'y' .

• According to the first condition –

$\\ \bf \implies \dfrac{x}{y} = \dfrac{10}{11}$

$\\ \bf \implies x = \dfrac{10}{11}y \: \: \: \: \: \: - - - - eq.(1)$

• According to the second condition –

$\\ \bf \implies x + y = 10$

• Using eq.(1) –

$\\ \bf \implies \dfrac{10}{11} y+ y = 10$

$\\ \bf \implies \dfrac{10 + 11}{11}( y)= 10$

$\\ \bf \implies \dfrac{21}{11}( y)= 10$

$\\ \large \implies{ \boxed{ \bf y= \dfrac{110}{21}}}$

• put the value of 'y' in eq.(1) –

$\\ \bf \implies x = \dfrac{10}{11} \left( \dfrac{110}{21} \right)$

$\\ \bf \implies x = \dfrac{10}{1} \left( \dfrac{10}{21} \right)$

$\\ \large \implies{ \boxed{ \bf x = \dfrac{100}{21}}}$

$\\ \rule{180}{7}$