8. If three times the larger of two numbers is divided by the smaller, weget 4 as the quotient and 8 as the remainder. If five times the smaller isdivided by the larger, we get 3 as the quotient and 5 as the remainder.Find the numbers.. Created by shashi4476. Math

Given,If three times the larger of two numbers is divided by the smaller then we get 4 as the quotient and 8 as the remainder.If Five years times the smaller is divided by the larger then we get 3 as the quotient and 5 as the remainder.To Find,The NumbersSolution : Suppose the First Number(Larger Number) be a And, Suppose the Second Number(Smaller Number) be b Therefore,According to the First Condition : If three times the larger of two numbers is divided by the smaller then we get 4 as the quotient and 8 as the remainder. 1) Equation According to the Second Condition :If Five years times the smaller is divided by the larger then we get 3 as the quotient and 5 as the remainder.║Now Put the Value of a From the Equation First ║║Now Put the Value of b in First Equation ║Therefore,

8. If three times the larger of two numbers is divided by the smaller, weget 4 a...

vikram991

Verified answer

Given,

If three times the larger of two numbers is divided by the smaller then we get 4 as the quotient and 8 as the remainder.
If Five years times the smaller is divided by the larger then we get 3 as the quotient and 5 as the remainder.

To Find,

The Numbers

Solution :

$\implies$ Suppose the First Number(Larger Number) be a

And, Suppose the Second Number(Smaller Number) be b

Therefore,

$\boxed{\underline{\sf{We \ Know \ that :}}}$

$\boxed{\sf{\pink{Divided = Divisor \times Quotient + Remainder }}}$

According to the First Condition :

If three times the larger of two numbers is divided by the smaller then we get 4 as the quotient and 8 as the remainder.

$\implies \sf{3a = b \times 4 + 8}$

$\implies \sf{3a = 4b + 8}$

$\implies \sf{a = \dfrac{4b + 8}{3}}$ 1) Equation

According to the Second Condition :

If Five years times the smaller is divided by the larger then we get 3 as the quotient and 5 as the remainder.

$\implies \sf{5b = a \times 3 + 5}$

$\implies \sf{5b = 3a + 5}$

║Now Put the Value of a From the Equation First ║

$\implies \sf{5b = 3(\dfrac{4b + 8}{3} ) + 5}$

$\implies \sf{5b = \dfrac{12b + 24}{3} + 5}$

$\implies \sf{5b = \dfrac{12b + 24 + 15}{3}}$

$\implies \sf{15b = 12b + 39}$

$\implies \sf{15b - 12b = 39}$

$\implies \sf{3b = 39}$

$\implies \sf{b = \dfrac{39}{3}}$

$\implies \boxed{\sf{b = 13}}$

║Now Put the Value of b in First Equation ║

$\implies \sf{a = \dfrac{4b + 8}{3}}$

$\implies \sf{a = \dfrac{4(13) + 8}{3}}$

$\implies \sf{a = \dfrac{52 + 8}{3}}$

$\implies \sf{a = \dfrac{60}{3}}$

$\implies \boxed{\sf{a = 20}}$

Therefore,

$\boxed{\large{\sf{\red{The \ Larger \ Number = a = 20}}}}$

$\boxed{\larger{\sf{\red{The \ Smaller \ Number = b = 13}}}}$

$\rule{200}2$

ButterFliee

$\huge{\underline{\underline{\bf{GIVEN:-}}}}$

three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder.
five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder.

$\huge{\underline{\underline{\bf{TO\:FIND:-}}}}$