Question
M, P and Q together started a business. M invested Rs. 6500 for 6 months, P invested Rs. 8400 for 5 months and Q invested Rs. 10000 for 3 months. M is working member for which he gets 5% of total profit extra. If the total gain is Rs. 7400, then Q's share is ?
Answer: Option A
M
:
P
:
Q
Capital →
6500
:
8400
:
10000
65
:
84
:
100
Time →
×6
:
×5
:
×3
390
:
420
:
300
Profit →
13
:
14
:
10
M's extra share on work in partner
$$\eqalign{
& = {\text{Rs}}.7400 \times \frac{5}{{100}} \cr
& = {\text{Rs}}{\text{.370 }} \cr
& {\text{Remaining profit}} \cr
& = {\text{Rs}}{\text{.}}\left( {{\text{7400}} - {\text{370}}} \right) \cr
& = {\text{Rs}}.\,7030 \cr} $$
According to the question,
(13 + 14 + 10) units = Rs. 7030
$$\eqalign{
& {\text{37 units}} = {\text{Rs}}{\text{. 7030}} \cr
& {\text{1 unit}} = {\text{Rs}}{\text{.}}\frac{{7030}}{{37}} \cr
& {\text{Profit of Q}} = {\text{10 units}} \cr
& = {\text{Rs}}.\frac{{7030}}{{37}} \times 10 \cr
& = {\text{Rs}}.\,1900 \cr} $$
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M
:
P
:
Q
Capital →
6500
:
8400
:
10000
65
:
84
:
100
Time →
×6
:
×5
:
×3
390
:
420
:
300
Profit →
13
:
14
:
10
M's extra share on work in partner
$$\eqalign{
& = {\text{Rs}}.7400 \times \frac{5}{{100}} \cr
& = {\text{Rs}}{\text{.370 }} \cr
& {\text{Remaining profit}} \cr
& = {\text{Rs}}{\text{.}}\left( {{\text{7400}} - {\text{370}}} \right) \cr
& = {\text{Rs}}.\,7030 \cr} $$
According to the question,
(13 + 14 + 10) units = Rs. 7030
$$\eqalign{
& {\text{37 units}} = {\text{Rs}}{\text{. 7030}} \cr
& {\text{1 unit}} = {\text{Rs}}{\text{.}}\frac{{7030}}{{37}} \cr
& {\text{Profit of Q}} = {\text{10 units}} \cr
& = {\text{Rs}}.\frac{{7030}}{{37}} \times 10 \cr
& = {\text{Rs}}.\,1900 \cr} $$
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