Percentage - Study Mode

[#431] To meet a government requirement, a bottler must test 5 percent of its spring water and 10 percent of its sparkling water for purity. If a customer ordered 120 cases of spring water and 80 cases of sparkling water, then what percent of all the cases must the bottler test before he can send it out ?
Correct Answer

(B) 7.0%

Explanation

Solution: Number of cases required to be tested : $$eqalign{
& = 5\% ,,{ ext{of}},,120 + 10\% ,,{ ext{of}},,80 cr
& = left( {frac{5}{{100}} imes 120}
ight) + left( {frac{{10}}{{100}} imes 80}
ight) cr
& = 6 + 8 cr
& = 14 cr} $$ ∴ Required percentage : $$eqalign{
& = left( {frac{{14}}{{120 + 80}} imes 100}
ight)\% cr
& = left( {frac{{14}}{{200}} imes 100}
ight)\% cr
& = 7\% cr} $$

[#432] A 14.4 kg gas cylinder runs for 104 hours when the smaller burner on the gas stove is fully opened while it runs for 80 hours when the larger burner on the gas stove is fully opened. Which of these value is the closest to the percentage difference in the usage of gas per hour, of the smaller burner over the larger burner ?
Correct Answer

(A) 23.07%

Explanation

Solution: Consumption of gas in the smaller burner in 1 hour : $$eqalign{
& = left( {frac{{14.4}}{{104}}}
ight){ ext{kg}} cr
& = frac{9}{{65}}{ ext{kg}} cr} $$ Consumption of gas in the larger burner in 1 hour : $$eqalign{
& = left( {frac{{14.4}}{{80}}}
ight){ ext{kg}} cr
& = frac{9}{{50}}{ ext{kg}} cr} $$ Difference in consumption : $$eqalign{
& = left( {frac{9}{{50}} - frac{9}{{65}}}
ight){ ext{kg}} cr
& = frac{{27}}{{650}}{ ext{kg}} cr} $$ Required percentage difference : $$eqalign{
& { ext{ = }}left( {frac{{27}}{{650}} imes frac{{50}}{9} imes 100}
ight)\% cr
& = left( {frac{{300}}{{13}}}
ight)\% cr
& = 23.07\% cr} $$

[#433] When water is changed into ice, its volume increases by 9%. If ice change into water, the percentage decrease in volume is :
Correct Answer

(A) $$8frac{{28}}{{109}}\% $$

Explanation

Solution: Let V denote the volume of 1 c.c. of water Then, volume of ice formed from it : = 109% of V = $$frac{109}{100}$$V When this ice change into water, decrease in volume : = $$frac{109}{100}$$V - V = $$frac{9}{100}$$V ∴ Decrease % : $$eqalign{
& = left( {frac{{9V}}{{100}} imes frac{{100}}{{109V}} imes 100}
ight)\% cr
& = frac{{900}}{{109}}\% cr
& = 8frac{{28}}{{109}}\% cr} $$

[#434] A tree increases annually by $$frac{1}{8}$$ of its height. By how much will it increase after $$2frac{1}{2}$$ years if it stands today 8 m high ?
Correct Answer

(A) 10.75 m

Explanation

Solution: Percentage annual increase $$eqalign{
& = left( {frac{1}{8} imes 100}
ight)\% cr
& = frac{{25}}{2}\% cr} $$ Height after $$2frac{1}{2}$$ years $$eqalign{
& = left[ {8{{left( {1 + frac{{25}}{{2 imes 100}}}
ight)}^2}left( {1 + frac{{25}}{{4 imes 100}}}
ight)}
ight]m cr
& = left( {8 imes frac{9}{8} imes frac{9}{8} imes frac{{17}}{{16}}}
ight)m cr
& = left( {frac{{1377}}{{128}}}
ight)m cr
& = 10.75,,m cr} $$

[#435] How many litres of a 30% alcohol solution should be added to 40 litres of a 60% alcohol solution to prepare a 50% solution ?
Correct Answer

(A) 20

Explanation

Solution: Let x litres of 30% alcohol solution be added. Then, 30% of x + 60% of 40 = 50% of (x + 40) ⇒ 30x + 60 × 40 = 50 (x + 40) ⇒ 30x + 2400 = 50x + 2000 ⇒ 20x = 400 ⇒ x = 20