(i) The sum of two numbers is 70 and thedifference between them is 50.

1.	(i) The sum of two numbers is 70 and thedifference between them is 50. Find thenumbers.
Answer» As per the given conditions, we have : • The sum of two numbers is 70. • The difference between them is 50. We need to calculate the numbers . Let us ASSUME the numbers as x and y respectively. According to the question, » The sum of two numbers is 70. $\longmapsto \sf {x + y = 70 }$ Let it be the equation (1). Also, the difference between them is 50. $\longmapsto \sf {x - y = 50 }$ From this EQUATION, we have : $\longmapsto \sf {x = 50 + y }$ Here, we get that x is equal to the sum of 50 and y. Substituting value of x from this equation into the equation (1). $\longmapsto \sf {x + y = 70 }$ $\longmapsto \sf {(50 +y) + y = 70 }$ $\longmapsto \sf {50 + y + y = 70 }$ $\longmapsto \sf {50 + 2y = 70 }$ $\longmapsto \sf {2y = 70 - 50}$ $\longmapsto \sf { 2y = 20 }$ $\longmapsto \sf { y = \cancel{\dfrac{20}{2}} }$ $\longmapsto \boxed{\sf { y = 10 }}$ Henceforth, value of y is 10. SUBSTITUTE the value of y in the equation (1) to find the value of y. $\longmapsto \sf {x + y = 70 }$ $\longmapsto \sf {x + 10 = 70 }$ $\longmapsto \sf {x = 70 -10 }$ $\longmapsto\boxed{ \sf {x = 60 }}$ Henceforth, value of x is 60. Therefore, • Two numbers ⇒ x and y ⇒ 10 and 60.