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ICSE Class X Math 2015 Solved Paper

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Question : 50
Total: 52
Sum of two natural numbers is 8 and the difference of their reciprocal is ‌
2
15
. Find the numbers.
Solution:  
Let 1 st no. be x and 2 nd be 8−x.
By the given condition,
‌‌
1
x
−‌
1
8−x
=‌
2
15

‌⇒‌‌‌
8−x−x
x(8−x)
=‌
2
15

‌⇒‌‌‌
8−2x
8x−x2
=‌
2
15

⇒‌‌120−30x‌=16x−2x2
2x2−46x+120‌=0
x2−23x+60‌=0
x2−20x−3x+60‌=0
x(x−20)−3(x−20)‌=0
(x−3)(x−20)‌=0
x=3‌ or ‌x‌=20‌ (not possible) ‌
1‌st ‌‌ no. ‌=3 ‌ and ‌2‌nd ‌‌ no. ‌‌=8−3=5.
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