If a/b = 1/3, b/c = 1/2, c/d = 6/7,e/f = 14/9 and d/e = 7/2 and, then what is the value of abc/def ?

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24 Feb 2017 Ratio

If a/b = 1/3, b/c = 1/2, c/d = 6/7,e/f = 14/9 and d/e = 7/2 and, then what is the value of abc/def ?

OPtion

1) 1/14
2) 3/14
3) 1/7
4) 3/7
5) 1/9
6) 2/9
7) 6/7
8) 2/21
9) 7/9
10)None of these

Solution

a/d = (a/b)*(b/c)*(c/d) = (1/3)*(1/2)*(6/7) = 1/7
b/e = (b/c)*(c/d)*(d/e) = (1/2)*(6/7)*(7/2) = 3/2
c/f = (c/d)*(d/e)*(e/f) = (6/7)*(7/2)*(14/9) = 14/3

So abc/def = (a/d)*(b/e)*(c/f) = (1/7)*(3/2)*(14/3) = 1

Option 10)

Correct Option: 10 Best Solution (10)

G.S.Kantharao   7 years AGO

a/b=1/3 --> a =b/3
b/c= 1/2 --> b = c/2
c/d= 6/7 --> c = 6d/7
d/e= 7/2 --> d = 7e/2
e/f = 14/9 --> e = 14f/9
a=b/3=(c/2)/3=c/6=(6d/7)/6=d/7=(7e/2)/7=e/2=(14f/9)/2=7f/9
-->a=b/3=c/6=d/7=e/2=f/(9/7) = k(let)
a=k,b=3k,c=6k,d=7k,e=2k,f=9k/7
abc/def = (k*3k*6k)/(7k*2k*9k/7)
=(1*3*6*7)/(7*2*9)=1
Hence the right option is 10.

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Baishali Roy   7 years AGO

Calculating we get, a/d=(a/b*b/c*c/d)=(1/3*1/2*6/7)=1/7
Same way, b/e=3/2, c/f=14/3
So, abc/def=(1/7*3/2*14/3)=1 (Ans). (Opt 10)... None of these answers

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Mukund Manohar   7 years AGO

abc/def = a/d * b/e *c/f
= (a/b * b/c * c/d) * (b/c * c/d * d/e) * (c/d * d/e * e/f)
= (1/7) * (3/2) * (14/3) = 1

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palak Jain   7 years AGO

e/f=14/9
d/e=7/2
now to make value of e same we multiply it by 7 both numerator and denominator
so, d/e=49/14
similarly, c/d=42/49
b/c=21/42
a/b=7/21
so , a:b:c:d:e:f=7:21:42:49:14:9
abc/def=7*21*42/49*14*9
=1
ans 10 none of these

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shraboni   7 years AGO

a/b×b/c×c/d=a/d=1/7
b/c×c/d×d/e=b/e=3/2
c/f=c/d×d/e×e/f =14/3
abc/def=a/d ×b/e×c/ f = 1/7 ×3/2 ×14/3
=1

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Ajay Sharma   7 years AGO

abc/def=(a/b)*(b/c)*(c/d)*(b/c)*(c/d)*(d/e)*(c/d)*(d/e)*(e/f)
=(1/3)*(1/2)*(6/7)*(1/2)*(6/7)*(7/2)*(14/9)*(6*7)*(7/2)
=1
hence none of these is correct option i.e option 10

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Kannan Ravi   7 years AGO

a/c=1/6 ,b/d=3/7,c/e=3/2,d/f=49/9

a/d=1/7,b/e=3/2,c/f=7/3 on multiplying

abc/def =1/2

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M.Mathan Kumar   7 years AGO

a/b*b/c*c/d=1/3*1/2*6/7=1/7
b/c*c/d*d/e=1/2*6/7*7/2=3/2
c/d*d/e*e/f=6/7*7/2*14/9=14/3
1/7*3/2*14/3=1

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Gulshan Kumar   7 years AGO

a/d=1/7
b/e=3/2
c/f=14/3
abc/def=1

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DIVYANSHU SHEKHAR   7 years AGO

(a/b)*(b/c)*(c/d)*(d/e)*(e/f)=(1/3)*(1/2)*(6/7)*(7/2)*(14/9)
=>(a/f)=7/9
(b/c)*(c/d)=(1/2)*(6/7)
=>(b/d)=3/7
(c/d)*(d/e)=(6/7)*(7/2)
=>(c/e)=3
So, (a/f)*(b/d)*(c/e)=(7/9)*(3/7)*3
=>abc/def=1

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