Ratio - Study Mode

[#226] If A varies directly proportional to C and B also varies directly proportional to C, which one of the following is not correct ?
Correct Answer

(B) $$left( {A - B} ight)alpha ,frac{1}{C}$$

Explanation

Solution: $$eqalign{
& { ext{A }}alpha { ext{ C and B }}alpha { ext{ C}} cr
& Rightarrow { ext{A}} = { ext{kC and B}} = { ext{mC}} cr
& { ext{for some constants k and m}}{ ext{.}} cr
& herefore A + B = kC + mC = left( {{ ext{k}} + { ext{m}}}
ight){ ext{C}} cr
& Rightarrow left( {A + B}
ight)alpha { ext{ C}}. cr
& { ext{A}} - { ext{B}} = { ext{kC}} - { ext{mC}} = left( {{ ext{k}} - { ext{m}}}
ight){ ext{C}} cr
& Rightarrow left( {A - B}
ight)alpha { ext{ C}}. cr
& sqrt {AB} = sqrt {kC imes mC} cr
& ,,,,,,,,,,,,,, = sqrt {{ ext{km}}{{ ext{C}}^2}} cr
& ,,,,,,,,,,,,,, = sqrt {{ ext{km}}.} { ext{C}} cr
& ,,,,,,,,,,,,,, = sqrt {{ ext{AB}}} { ext{ }}alpha { ext{ C}} cr
& = frac{{ ext{A}}}{{ ext{B}}} = frac{{{ ext{kC}}}}{{{ ext{mC}}}} cr
& ,,,,,,,,,,, = frac{{ ext{k}}}{{ ext{m}}} = { ext{Constant}}{ ext{.}} cr} $$

[#227] Arrange the number a = $$frac{7}{{10}},$$ b = $$frac{5}{8},$$ c = $$frac{2}{3}$$ in descending order = ?
Correct Answer

(B) a > c > b

Explanation

Solution: $$eqalign{
& a = frac{{7 imes 24}}{{10 imes 24}} = frac{{168}}{{240}} cr
& b = frac{{5 imes 30}}{{8 imes 30}} = frac{{150}}{{240}} cr
& c = frac{{2 imes 80}}{{3 imes 80}} = frac{{160}}{{240}} cr
& { ext{The descending order}} cr
& { ext{ = }}a > c > b cr} $$

[#228] A man spends his two months income in three months time, if his monthly income is 6000 , then his annual savings is = ?
Correct Answer

(B) Rs. 24000

Explanation

Solution: If he spends two months income in three months. It means he saves the third month income in three months. He saves Rs. 6000 in every 3 months. So, in one year he saves Rs. 4 × 6000 = Rs. 24000

[#229] A box has 1 rupee, 50 paise and 25 paise coins in the ratio 3 : 2 : 5 worth Rs. 252. The number of 25 paise coins in the box is = ?
Correct Answer

(C) 240

Explanation

Solution: Ratio of coin's Rs. 1 : 50p : 25P = 3 : 2 : 5 Ratio of coin's value Rs. 1 : 50p : 25p (value) = 3 : 1 : 1.25 (Multiply by 4 to remove the fraction value in above ratio) i.e Rs. 1 : 50p : 25p (value) = 12 : 4 : 5 Value of 25p coin in Rs. 252 = $$frac{5}{{21}} imes 252 = 60 $$ Number of 25p coin is = 60 × 4 = 240

[#230] The falling height of an object is proportional to the square of the time. One object falls 64 cm in 2 sec then in 6 sec from how much height the object will fall ?
Correct Answer

(D) 576 cm

Explanation

Solution: h α t 2 ⇒ h = kt 2 for some constant k ⇒ 64 = k × 2 2 = 4k ⇒ k = 16. Let the required height be x cm. Then, = x = 16 × 6 2 = (16 × 36) cm = 576 cm.