Partnership - Study Mode

[#91] P and Q start a shop with a capital of Rs. 1,50,000 and Rs. 4,50,000 respectively. After a year, out of the profit of Rs. 1,60,000, P gets his share of profit plus some money that is not a part of the profit, as his salary. If P gets a total of Rs. 70,000, what is the salary (in Rs.) he received?
Correct Answer

(B) 30,000

Explanation

Solution: [x08egin{array}{*{20}{c}}
{ ext{P}}&{}&{ ext{Q}} \
{1,50,000}&:&{4,50,000} \
1&:&3
end{array}] 4 → 1,60,000 1 → 40,000 ∴ Salary of P = 70,000 - 40,000 = Rs. 30,000

[#92] A, B and C started a business with initial investments of Rs. 20000, Rs. 25000 and Rs. 10000, respectively. After 5 months from start, A invested Rs. 4000 more. After 6 months from start, C invested Rs. 8000 more. After 4 months from start, B withdrew Rs. 8000. At the end of the year, they will receive a profit of Rs. 'x'. In what ratio they will share the profits?
Correct Answer

(A) 67 : 59 : 42

Explanation

Solution: [x08egin{array}{*{20}{c}}
{ ext{A}}&:&{ ext{B}}&:&{ ext{C}} \
{20,000 imes 5 + 24,000 imes 7}&:&{25,000 imes 4 + 17,000 imes 8}&:&{10,000 imes 6 + 18,000 imes 6} \
{268}&:&{236}&:&{168} \
{67}&:&{59}&:&{42}
end{array}]

[#93] Person A started a business by investing Rs. 65,000. After a few months, B joined him by investing Rs. 50,000. Three months after the joining of B, C joined the two with an investment of Rs. 55,000. At the end of the year, A got 50% of profit as his share. For how many months did A alone finance the business?
Correct Answer

(B) 3

Explanation

Solution: A got 50% of share and remaining 50% divided in B and C ∴ 10x + 30 + 11x = 156 ⇒ 21x = 126 ⇒ x = 6 B did for = 9 months C did for = 6 months ∴ A alone did business for = 3 months

[#94] A, B and C started a business in partnership. Initially, A invested Rs. 29,000, while B and C invested Rs. 25,000 each. After 4 months, A withdrew Rs. 3,000. After 2 more months, C invested Rs. 12,000 more. Find the share of C (in Rs.) in the profit of Rs. 33,200 at end of the year.
Correct Answer

(D) 12,400

Explanation

Solution: [x08egin{array}{*{20}{c}}
{ ext{A}}&{}&{ ext{B}}&{}&{ ext{C}} \
{29,000}&{}&{25,000}&{}&{25,000} \
{29}&{}&{25}&{}&{25} \
{left( {29 imes 4 + 26 imes 8}
ight)}&{}&{left( {25 imes 12}
ight)}&{}&{left( {25 imes 6 + 37 imes 6}
ight)} \
{81}&:&{75}&:&{93} \
{27}&:&{25}&:&{31}
end{array}] $$eqalign{
& 83,{ ext{unit}} o 33,200 cr
& 1{ ext{ unit}} o frac{{33,200}}{{83}} cr
& 31,{ ext{unit}} o frac{{33,200}}{{83}} imes 31 cr
& = { ext{Rs}}{ ext{. }}12,400{ ext{ Answer}} cr} $$

[#95] The ratio of the investments of A and B in a business is 7 : 5, and the ratio of their profits at the end of a year is 2 : 5. If A invested the money for 6 months, then for how much time (in months) has B invested his money?
Correct Answer

(C) 21

Explanation

Solution: $$eqalign{
& { ext{Time}} = frac{{{ ext{Profit}}}}{{{ ext{Capital}}}} cr
& { ext{A's time}} = frac{2}{7}{ ext{ units}} cr
& { ext{B's time}} = frac{5}{5} = 1{ ext{ unit}} cr
& frac{2}{7}{ ext{ units}} = 6{ ext{ months}} cr
& 1{ ext{ unit}} = 6 imes frac{7}{2} = 21,{ ext{months}} cr} $$