Sum of two numbers is 133. If one number is six times the other, then 2/3 of the larger number is
A.78
B.95
C.104
D.76
Answers
Answer:
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The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their squares.
Medium
Solution
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Correct option is A)
Let two number be a and b,
According to question,we get,
a+b=7
a
3
+b
3
=133
Now,
(a+b)
3
=a
3
+b
3
+3ab(a+b)
=>7
3
=133+3ab(7)
=>
21
343−133
=ab
=>ab=
21
210
=>ab=10
Now,
(a+b)
2
=a
2
+b
2
+2ab
=>7
2
=a
2
+b
2
+2(10)
=>a
2
+b
2
=49−20
=>a
2
+b
2
=29
Answer:
Option D) 76.
Step-by-step explanation:
Given :
- Sum of two numbers is 133.
- One number is six times the other.
To find :
2/3 of the larger number
Solution :
Let the smaller number be 'x'.
Then, the larger number = 6 times the smaller number
larger number = 6x
Sum of the two numbers = 133
x + 6x = 133
7x = 133
x = 133/7
x = 19
Therefore, the smaller number = 19
The larger number = 6(19) = 114
2/3 of the larger number :
⇒ 2/3 × 114
⇒ 2 × 38
⇒ 76
∴ The required answer is 76.