Percentage - Study Mode

[#286] A shopkeeper first raises the price of Jewellery by x% then he decreases the new price by x%. After such up down cycle, the price of a Jewellery decreased by Rs. 21025. After a second up down cycle the Jewellery was sold for Rs. 484416. What was the original price of the jewellery.
Correct Answer

(C) Rs. 5,25,625

Explanation

Solution: Let the initial price = Rs. 10000p Price after first increment = 10000p + 100xp Price after first decrement = 10000p + 100xp - (100px + px 2 ) = 10000p - px 2 Now, total decrement, px 2 = 21025 . . . . . (1) Price after second increment, = 10000p - px 2 + 100xp - $$frac{{{ ext{p}}{{ ext{x}}^3}}}{{100}}$$ Price after second increment, = 10000p - p 2 + 100xp - $$frac{{{{ ext{p}}^3}}}{{100}}$$ - 100xp + $$frac{{{ ext{p}}{{ ext{x}}^3}}}{{100}}$$ - px 2 + $$frac{{{ ext{p}}{{ ext{x}}^4}}}{{10000}}$$ = 10000p - 2px 2 + $$frac{{{ ext{p}}{{ ext{x}}^2}}}{{10000}}$$ = 484416 . . . . . . (2) On solving equation (1) and (2), We get x = 20 Substituting back we get, p = 5,25,625

[#287] A company has 12 machines of equal efficiency in its factory. The annual manufacturing expenses are Rs. 24,000 and the establishment charges are Rs. 10,000. The annual output of the company is Rs. 48,000. The annual output and manufacturing costs are directly proportional to the no. of machines while the share holders get the 10% profit, which is directly proportional to the annual output of the company. If 8.33% of machines remained close throughout the year. Then the percentage decrease in the amount of share holders is :
Correct Answer

(A) 14.28%

Explanation

Solution: No. of Machines Output Manuf. cost Est. cost Total cost Profit 12 48, 000 24, 000 10, 000 34, 000 14, 000 11 44, 000 22, 000 10, 000 32, 000 12, 000 Profit, = Output - total cost
= 44000 - 32000
= Rs. 12000
Initial value of share holders,
= 14000 $$ imes frac{{10}}{{100}}$$
= Rs. 1400
New value of share holders,
= 12000 $$ imes frac{{10}}{{100}}$$
= Rs. 1200 Decrease in Share holder value = 1400 - 1200 = 200 percentage decrease in the value of shareholders is : $$eqalign{
& = frac{{200 imes 100}}{{1400}} cr
& = 14.28\% cr} $$

[#288] Every month a man consumes 25 kg rice and 9 kg wheat. The price of rice is 20% of the price of wheat and thus he spends total Rs. 350 on the rice and wheat per month. If the price of wheat is increased by 20% then what is the percentage reduction of rice consumption for the same expenditure of Rs. 350? Given that the price of rice and consumption of wheat is constant :
Correct Answer

(C) 36%

Explanation

Solution: Let the price of wheat is x per kg. Then price of wheat will be 5x per kg.
Expenditure on rice = 25 × x = 25x
Expenditure of wheat = 9 × 5x = 45x
Total cost,
25x + 45x = 350
70x = 350
x = 5
Hence, price of Rice = Rs. 5 per kg. Price of wheat = 25 per kg. Now, price of wheat = 25 ---- 20% ↑----> Rs. 30 per kg. Let the new amount of rice is N kg, then N*5 + 9*30 = 350 N = 16 kg. % decrease in the amount of rice $$eqalign{
& = frac{{left( {25 - 16}
ight) imes 100}}{{25}} cr
& = 36\% cr} $$

[#289] The price of raw materials has gone up by 15%, labor cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be reduction in the usage of raw materials so as to keep the cost same?
Correct Answer

(B) 17%

Explanation

Solution: Let the initial cost of raw material be 100. So, initial labor cost was 25 and net cost was 125
Now, 15% increment in raw materials cost and labor cost has gone up to 30% from 25 % Raw material cost = 115 And Labor cost = (115 × 30%) = 34.5 So, New net cost, = 115 + 34.5 = 149.5 Difference of labor cost = 149.5 - 125 = 24.5 % reduction = $$frac{{24.5 imes 100}}{{149.5}}$$ xa0xa0= 17%(approx.)

[#290] A sales executive gets 20% bonus of the total sales value and 10% commission besides the bonus on the net profit after charging such commission. If the total sales value be Rs. 10 lakh per annum and the total profit of the company be Rs. 1.32 lakh, then his total earning per annum will be, given that he is not entitled to receive any fixed salary from the company :
Correct Answer

(C) 2.12 lakh

Explanation

Solution: $$eqalign{
& { ext{His bonus}}, cr
& = frac{{ {20 imes 1000000} }}{{100}} cr
& = 2, ext{lakh} cr
& { ext{Total}},{ ext{profit}} = { ext{Net}},{ ext{profit}} + frac{{ {10 imes { ext{net}},{ ext{profit}}} }}{{100}} cr
& 1.32, ext{lakh} = { ext{Net}},{ ext{profit}} imes left[ {1 + {frac{{10}}{{100}}} }
ight] cr
& { ext{Net}},{ ext{profit}} = frac{{132000}}{{1.1}} = 120000 cr
& { ext{Commission}}, cr
& = left( {{ ext{Total}},{ ext{profit}} - { ext{Net}},{ ext{profit}}}
ight) cr
& = 132000 - 120000 cr
& = 12000 cr
& { ext{Hence}}, { ext{his}},{ ext{total}},{ ext{earnings}} cr
& = 2, ext{lakh} + 12000 cr
& = Rs.,212000 cr} $$