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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?
Answer & Solution
Correct Answer:
Option
B
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,
$$\eqalign{ & \frac{{14x}}{{8y}} = \frac{5}{7} \Rightarrow 98x = 40y \cr & \Rightarrow y = \frac{{49x}}{{20}} \cr & {\text{And, }}\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \Rightarrow 112x = 35z \cr & \Rightarrow z = \frac{{112x}}{{35}} = \frac{{16x}}{5} \cr & {\text{So}}\,x:y:z = x:\frac{{49x}}{{20}}:\frac{{16x}}{5} \cr & ({\text{Multiply by 20}}) \cr & \Rightarrow 20:49:64 \cr} $$
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now,
$$\eqalign{ & \frac{{14x}}{{8y}} = \frac{5}{7} \Rightarrow 98x = 40y \cr & \Rightarrow y = \frac{{49x}}{{20}} \cr & {\text{And, }}\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \Rightarrow 112x = 35z \cr & \Rightarrow z = \frac{{112x}}{{35}} = \frac{{16x}}{5} \cr & {\text{So}}\,x:y:z = x:\frac{{49x}}{{20}}:\frac{{16x}}{5} \cr & ({\text{Multiply by 20}}) \cr & \Rightarrow 20:49:64 \cr} $$
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LoginThen, 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.
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
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
so, 56 of 5/14 = 20. similarly, 56 of 7/8=49. and, 56 of 8/7=64.
so, guys, is it clear now???
280:49:64
Is it wrong
actually i not getting that Point... 20 ??? Comes from where?
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
ANSWAR WILL BE 10;8;8