the ages of simmy and Jimmy are in the ratio 6:8 five years from now t

1.	the ages of simmy and Jimmy are in the ratio 6:8 five years from now the ratio of their ages will be 4:5 find their present ages
Answer» ong>⇒ GIVEN: Current ages of SIMMY and Jimmy are in the ratio 6:8. Five years later, their ages are in the ratio 4:5. ⇒ To Find: Their current ages. ⇒ Solution: It is given that the current ages of Simmy and Jimmy are in the ratio 6:8. Assuming the ages as 6x and 8x, It can be represented in fractional form as: $\sf{\implies\:6:8=\dfrac{6x}{8x}}$ So, five years from now, their ages are 6x + 5 and 8x + 5 respectively. It is given that, 5 years later, their ages are in the ratio 4 : 5. Writing the given statements in equational form: $\sf{\implies\dfrac{6x+5}{8x+5}=\dfrac{4}{5}}$ Doing cross multiplication: $\sf{\implies5(6x+5)=4(8x+5)}$ Opening the BRACKETS: $\sf{\implies30x+25=32x+20}$ GROUPING the constants and variables: $\sf{\implies30x-32x=20-25}$ $\sf{\implies-2x=-5}$ $\sf{\implies\:x=\dfrac{5}{2}}$ The value of x is 5/2. So, $\sf{\maltese\:Simmy=6x=6\times\dfrac{5}{2}}$ $\sf{=3\times5}$ $\bf{=15\:years\:old.}$ $\sf{\maltese\:Jimmy=8x=8\times\dfrac{5}{2}}$ $\sf{=4\times5}$ $\bf{20\:years\:old.}$ Therefore the ages of Simmy and Jimmy are 15 and 20 years respectively.