2400 ₹ is divided into men and women, whose total number is 95. The ratios received by all men and women are 6: 5 but it has a ratio of 4: 3 in the individual portion. What is the number of women?
Answers
Step-by-step explanation:
The number of men is 30
Step-by-step explanation:
Let x and y be the total amount of money received by men and women respectively.
Then,
x+y =180
As per data,
x : y = 5 : 4
x=5k , y= 4k
x+y=180
This implies
5k+4k=180
9k =180
k=20
x = 5(20)= 100
y = 4(20) = 80
Let a and b be the number of men and women respectively.
Then,
a+b=66
As per data,
\frac{100}{a}:\frac{80}{b}=3:2
a
100
:
b
80
=3:2
\frac{100}{a}:\frac{80}{66-a}=3:2
a
100
:
66−a
80
=3:2
\frac{\frac{100}{a}}{\frac{80}{66-a}}=\frac{3}{2}
66−a
80
a
100
=
2
3
\frac{100(66-a)}{80a}=\frac{3}{2}
80a
100(66−a)
=
2
3
\frac{5(66-a)}{4a}=\frac{3}{2}
4a
5(66−a)
=
2
3
\frac{330-5a)}{4a}=\frac{3}{2}
4a
330−5a)
=
2
3
\frac{330-5a)}{2a}=\frac{3}{1}
2a
330−5a)
=
1
3
330-5a=6a330−5a=6a
330=11a330=11a
a=\frac{330}{11}a=
11
330
a=30a=30
Therefore , the number of men is 30