Ratio - Study Mode

[#271] Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
Correct Answer

(B) 33

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{number}},{ ext{be}},3x,{ ext{and}},5x cr
& { ext{Then}},,frac{{3x - 9}}{{5x - 9}} = frac{{12}}{{23}} cr
& Rightarrow 23left( {3x - 9}
ight) = 12left( {5x - 9}
ight) cr
& Rightarrow 9x = 99 cr
& Rightarrow x = 11 cr
& herefore { ext{The}},{ ext{smaller}},{ ext{number}} cr
& = {3 imes 11} cr
& = 33 cr} $$

[#272] In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?
Correct Answer

(C) 150

Explanation

Solution: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively Then, sum of their values $$eqalign{
& = Rs.,left( {frac{{25x}}{{100}} + frac{{10 imes 2x}}{{100}} + frac{{5 imes 3x}}{{100}}}
ight) cr
& = Rs.,frac{{60x}}{{100}} cr
& herefore frac{{60x}}{{100}} = 30 Leftrightarrow x = frac{{30 imes 100}}{{60}} = 50 cr
& { ext{Hence,}},{ ext{the}},{ ext{number}},{ ext{of}},{ ext{5p}},{ ext{coins}} cr
& = left( {3 imes 50}
ight) cr
& = 150 cr} $$

[#273] What is the ratio in Rs. 2.80 and 40 paise?
Correct Answer

(C) 7 : 1

Explanation

Solution: Rs. 2.80 = 280 paise ∴ Required ration = 280 : 40 = 7 : 1

[#274] A person spends Rs. 8100 in buying some tables at Rs. 1200 each and some chairs at Rs. 300 each. The ratio of the number of chairs to that of tables when the maximum possible number of tables is purchased,
Correct Answer

(A) 1 : 2

Explanation

Solution: Maximum possible number of tables = 6 [∵ 1200 × 6 = 7200] Number of chairs purchased $$eqalign{
& { ext{ = }}frac{{{ ext{8100}} - { ext{7200}}}}{{{ ext{300}}}}{ ext{ = }}frac{{{ ext{900}}}}{{{ ext{300}}}}{ ext{ = 3}}{ ext{}} cr
& { ext{Hence,}} cr
& { ext{Required ratio}} = { ext{3}}:{ ext{6}} cr
& { ext{ = 1}}:{ ext{2}} cr} $$

[#275] If $$x = frac{1}{3}y$$ xa0 and $$y = frac{1}{2}z{ ext{,}}$$ xa0 then x : y : z is equal to = ?
Correct Answer

(C) 1 : 3 : 6

Explanation

Solution: $$eqalign{
& x = frac{1}{3}y,,{ ext{and }}y = frac{1}{2}z cr
& frac{x}{y} = frac{1}{3},{ ext{and }}frac{y}{z} = frac{1}{2} cr
& x:y = 1:3 cr
& y:z = 1:2 imes 3,({ ext{multiply}}) cr
& i.e.,y:z = 3:6 cr
& herefore x:y:z = 1:3:6 cr} $$