Verbal Reasoning - Arithmetic Reasoning - Discussion

Discussion :: Arithmetic Reasoning - Section 1 (Q.No.43)

43. 

In a family, the father took 1/4 of the cake and he had 3 times as much as each of the other members had. The total number of family members is

[A]. 3
[B]. 7
[C]. 10
[D]. 12

Answer: Option C

Explanation:


Suresh said: (Apr 1, 2013)  
How there could be (x+1) members why can't x members?

Apeksha said: (Aug 24, 2013)  
Suppose there is 100 kg of cake, then father's share = 25kg.

So each family member will get 25/3 kg.

Let x be the no.of members.

Therefore,

x(25/3) = 75.

x = 9.

Total members 9+1(father).

Teja said: (Oct 20, 2014)  
Let total number of family members be a.

Total amount of cake be x.

1/4x is fathers part.

3/4x is remaining members part (a-1).

1/4x = 3(3/4x)/a-1 (remaining members excluding father).

a-1 = 9.

a = 10.

Ravi. U S said: (May 3, 2017)  
This type of problem can be solved still easier way.

Father had 1 part of a cake in 4 parts. Remaining parts are 3. Multiply the remaining parts with the number of times it is more. As given in the problem 3*3= 9. Including father, it is 10 members.

Gauri said: (Sep 21, 2017)  
Nice @Ravi.

Arjun said: (Apr 2, 2018)  
Let the family members b x.

Father ate 1/4 of the cake;
Rest members got 3/4x,
ATQ, the father had 3 times more than other members share i.e 3/4,
Now,
3(3/4x) = 1/4,
3/4x = 1/12,
36 = 4x,
X = 9,
9 + 1(father) = 10 total family member.

Tharini said: (Jun 30, 2019)  
Good explanation. Thanks @Ravi.

Kanchik said: (Dec 11, 2019)  
@Ravi suberb.

Kavi said: (Oct 23, 2020)  
Thanks @Ravi.

Rakesh said: (May 20, 2021)  
Nice, thanks @Ravi.

Dhruvan said: (Jul 14, 2021)  
@Arjun.

Why take x for 3/4 term and not for 1/4 term? I think x term will be both sides of the eqn.

Isa said: (Oct 14, 2021)  
As per the question, each and every other 1/4 of the cake was shared by 3 people as compared to that of their father.

Remaining quarters are 3*3(people) for all 3 quarters = 9 + 1(Father) = 10.

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