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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 ?

a) Rs. 1900
b) Rs. 2100
c) Rs. 3200
d) Data are incomplete

Answer: a
Explanation:
    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
$$\eqalign{ & = {\text{Rs}}.7400 \times \frac{5}{{100}} \cr & = {\text{Rs}}{\text{.370 }} \cr & {\text{Remaining profit}} = {\text{Rs}}{\text{.}}\left( {{\text{7400}} – {\text{370}}} \right) \cr & = {\text{Rs}}.\,7030 \cr} $$
(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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