The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is:
(a) 15, (b) 20, (c) 30, (d) 32, (e) 33
Answers
Answer:
Step-by-step explanation:
Solution:
Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2/3.
x/y = 2/3.
x = 2/3 × y.
x = 2y/3.
The ratio of the second to the third is 5/8.
y/z = 5/8.
z/y = 8/5.
z = 8/5 × y.
z = 8y/5.
Put the value of x = 2y/3 and z = 8y/5 in (i).
2y/3 + y + 8y/5 = 98
49y/15 = 98.
49y = 98 × 15.
49y = 1470.
y = 1470/49.
y = 30 .
Therefore, the second number is 30.
Answer: (c)
Answer:
OPTION C IS CORRECT ANSWER
Step-by-step explanation:
Let the first number be
n
1
Let the second number be
n
2
Let the third number be
n
3
Given that
n
1
n
2
=
2
3
Given that
n
2
n
3
=
5
8
Given that
n
1
+
n
2
+
n
3
=
98
.................................(1)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider
n
1
n
2
=
2
3
Write this as
3
n
1
=
2
n
2
So
n
1
=
2
3
n
2
.................................................(2)
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider
n
2
n
3
=
5
8
Write this as
8
n
2
=
5
n
3
So
n
3
=
8
5
n
2
......................................................(3)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute (3) and (2) into (1) giving:
n
1
+
n
2
+
n
3
=
98
→
2
3
n
2
+
n
2
+
8
5
n
2
=
98
⇒
n
2
(
10
+
1
+
24
15
)
=
98
⇒
n
2
=
30