John and Jivan together have 45 marbles .Both of them lost 5 marbles each and the product of number of marbles they have now is 124. Find out how many marbles did they start with.
Solution : Let us assume , Number of marbles John has be ‘x’. Jivan has 45 – x . John = x – 5 Jivan = 45 –(x-5) = 40 – x. (x-5)(40-x) = 0 40x – 200 – x^{2}
+ 5x = 0 . 45x – x^{2}
– 200 = 0 . x^{2}
– 40 x – 5(x-40) = 0 x(x-40) – 5 (x-40) = 0 . (x-5) (x-40) = 0 . X = 5 0r x = 40 .
John and Jivan together have 45 marbles .Both of them lost 5 marbles each and the product of number of marbles they have now is 124. Find out how many marbles did they start with.
Solution : Let us assume , Number of marbles John has be ‘x’. Jivan has 45 – x . John = x – 5 Jivan = 45 –(x-5) = 40 – x. 40x – 200 –x^{2}
x = 9 . Condition (1) , x = 9 John x i.e x = 9 , Jivan 45 –x i.e 45 -9 = 36 John = 9 marbles and Jivan = 36 marbles. Condition (ii) , x = 36 John has 36 marbles , Jivan has 45 -36 = 9 marbles . John = 36 marbles , Jivan = 9 marbles. Problem :
Find the two numbers whose sum is 27 and the product is 182.
Solution : Let us assume one number as ‘x’ , Other number is 27 – x . x(27-x) = 182 \Rightarrow
x = 13 or x = 14 x = 13 27-13 = 14 . Two numbers are 13 and 14 . Problem (2) : Find two consecutive positive numbers or integers , sum of whose squares is 365 . Solution :Let us assume one integer as x and the other is x + 1 . (x)^{2} + (x+1)^{2}
x = -14 . x +1 = -14 +1 = -13 therefore Two numbers are -13 and -14 . Problem (3 ) : The altitude of a right angle triangle is 7cms less than its base . If hypotenuse is 13 cms . Find the other two sides ? Solution : Let the base of the triangle be ‘x’ cms , Altitude = (x-7) cms . Base ^{2}
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