Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
A. 5 : 7 : 8
B. 20 : 49 : 64
C. 38 : 28 : 21
D. None of these
Answer: Option B
Solution(By Examveda Team)
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.Then, 14x : 8y : 7z = 5 : 7 : 8.
Now,
$$\eqalign{ & \frac{{14x}}{{8y}} = \frac{5}{7} \Rightarrow 98x = 40y \cr & \Rightarrow y = \frac{{49x}}{{20}} \cr & {\text{And, }}\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \Rightarrow 112x = 35z \cr & \Rightarrow z = \frac{{112x}}{{35}} = \frac{{16x}}{5} \cr & {\text{So}}\,x:y:z = x:\frac{{49x}}{{20}}:\frac{{16x}}{5} \cr & ({\text{Multiply by 20}}) \cr & \Rightarrow 20:49:64 \cr} $$
This Question Belongs to Arithmetic Ability >> Partnership
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Related Questions on Partnership
A. 5 : 7 : 8
B. 20 : 49 : 64
C. 38 : 28 : 21
D. None of these
A. Rs. 40000
B. Rs. 50000
C. Rs. 60000
D. Rs. 70000
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x:8y:7z=5:7:8.
Now,
8y
14x
=
7
5
⇔98x=40y⇔y=
20
49
x
And,
7z
14x
=
8
5
⇔112x=35z⇔z=
35
112
x=
5
16
x.
∴x:y:z=x:
20
49
x:
5
16
x=20:49:64.
How is it possible? Why 12 is multiple with 490000 and why only 6 multiple with 35000?
Profit= investment×time
Investment= time÷profit
A:B:C= 5:7:8÷14:8:7
A×14:B×8:C×7=5:7:8
A=5÷14, B=7÷8, C=8÷7
LCM of14, 8,7= 56
A=5÷14×56= 20 and same for others
Thanks for help
Good mathod to solve
A×14:B×8:C×7=5:7:8
A×14:B×8=5:7
A/B=20/49
B×8:C×7=7:8
B/C=49/64
A:B:C=20:49:64
why it is multiplied by 20
is there any video lecture to understand these types of question for beginners?if it is then please share link with me.Thanks.
the l.c.m of 14,8 and 7 is 56.
so, 56 of 5/14 = 20. similarly, 56 of 7/8=49. and, 56 of 8/7=64.
so, guys, is it clear now???
how 64 comes?
any short method
My ans is
280:49:64
Is it wrong
actually i not getting that Point... 20 ??? Comes from where?
Remember the formula Profit= Investment* Time period
Thus in this case it would be I=P/T
5/14:7/8:8/7
LCM of denominators being 56 multiply throughout by 56 and the answer should be 20:49:64
WRONG
ANSWAR WILL BE 10;8;8
sir any eacy step to this
is there any shortcut to this.
how 64 is come?