Percentage - Study Mode

[#261] The value of a machine depreciates at the rate of 12 percent per annum. It was purchased three years ago. Its present value is Rs. 29644.032. What was the purchase price of the machine ?
Correct Answer

(C) Rs. 43500

Explanation

Solution: Purchase price : $$eqalign{
& = { ext{Rs}}{ ext{.}}left[ {frac{{29644.032}}{{{{left( {1 - frac{{12}}{{100}}}
ight)}^3}}}}
ight] cr
& = { ext{Rs}}{ ext{.}}left( {29644.032 imes frac{{25}}{{22}} imes frac{{25}}{{22}} imes frac{{25}}{{22}}}
ight) cr
& = { ext{Rs}}.43500 cr} $$

[#262] From 5 litres of a 20% solution of alcohol in water, 2 litres of solution is taken out and 2 litres of water is added to it. Find the strength of alcohol in the new solution.
Correct Answer

(B) 12%

Explanation

Solution: Quantity of alcohol in 5 litres solution = 20% of 5 litres = 1 litre Quantity of alcohol removed = 20% of 2 litres = 400 ml Quantity of alcohol in new solution : = (1000 - 400)ml = 600 ml ∴ Strength of alcohol in new solution $$eqalign{
& = left( {frac{{600}}{{5000}} imes 100}
ight)\% cr
& = 12\% cr} $$

[#263] A man ordered a length of rope by telephone from his nearest hardware shop. But when a worker in the shop brought the rope, he found that the man on the telephone had miswritten the order by interchange feet and inches. As a result of this, the length of rope received was only 30% of the length he had ordered. The length of the rope which the man ordered was between :
Correct Answer

(C) 9 ft and 2 inches

Explanation

Solution: Suppose the man ordered x feet y inches of the rope. Since x and y represent inches in the miswritten and actual order respectively, so each one of x and y is less than 12. [ $$x08ecause $$1 feet = 12 inches] Actual order = x feet y inches = (12x + y) inches Miswritten order = y feet x inches = (12y + x) inches ∴ (12y + x) = 30% of (12x + y) = $$frac{3}{10}$$ (12x + y) ⇒ 10 (12y + x) = 3 (12x + y) ⇒ 26x = 117y ⇒ $$frac{x}{y}$$ = $$frac{117}{26}$$ = $$frac{9}{2}$$ Since x < 12, y < 12, so x = 9, y = 2 Hence, the man ordered 9 feet 2 inches of rope.

[#264] 60% of 264 is the same as :
Correct Answer

(B) 15% of 1056

Explanation

Solution: 60% of 264 $$eqalign{
& = left( {frac{{60}}{{100}} imes 264}
ight) cr
& = 158.40 cr} $$ 10% of 44 $$eqalign{
& = left( {frac{{10}}{{100}} imes 44}
ight) cr
& = 4.40 cr} $$ 15% of 1056 $$eqalign{
& = left( {frac{{15}}{{100}} imes 1056}
ight) cr
& = 158.40 cr} $$ 30% of 132 $$eqalign{
& = left( {frac{{30}}{{100}} imes 132}
ight) cr
& = 39.60 cr} $$ ∴ 60% of 264 = 15% of 1056

[#265] The number which exceeds 16% of it by 42 is :
Correct Answer

(A) 50

Explanation

Solution: Let the number be $$x$$ Then, $$eqalign{
& x - 16\% ,,{ ext{of}},x = 42 cr
& Leftrightarrow x - frac{{16}}{{100}}x = 42 cr
& Leftrightarrow x - frac{4}{{25x}} = 42 cr
& Leftrightarrow frac{{21}}{{25}}x = 42 cr
& Leftrightarrow x = left( {frac{{42 imes 25}}{{21}}}
ight) cr
& Leftrightarrow x = 50 cr} $$