Ratio - Study Mode
[#261] A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a pair of black socks is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50% . The ratio of the number of black and brown pairs of socks in the original order was = ?
Correct Answer
(B) 1 : 4
Explanation
Solution: Black : Brown Pairs 4 : x Price 2 : 1 8 : x Original bill = 8 + x Black : Brown Pairs x : 4 Price 2 : 1 2x : 4 New bill = 2x + 4 According to the question, $$eqalign{
& herefore { ext{3}}left( {8 + x}
ight) = 2left( {2x + 4}
ight) cr
& Rightarrow 24 + 3x = 4x + 8 cr
& Rightarrow x = 16 cr
& herefore { ext{ Brown pairs}} = 16 cr
& herefore { ext{Black pairs}} = 4 cr
& herefore { ext{Ratio}} Rightarrow 1:4 cr} $$
[#262] The ratio of age of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be = ?
Correct Answer
(C) $$frac{{17}}{{18}}$$
Explanation
Solution: Ratio of ages of Boys A and B $$eqalign{
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,{ ext{A}},,,:,,,{ ext{B}} cr
& { ext{Present age }}5x,,,:,,,6x cr
& herefore { ext{After two years }} cr
& herefore frac{{5x + 2}}{{6x + 2}} = frac{7}{8} cr
& Rightarrow 40x + 16 = 42x + 14 cr
& Rightarrow 2x = 2 cr
& Rightarrow x = 1 cr
& herefore { ext{Present age }} cr
& { ext{A}} = 5 imes 1 = 5 cr
& { ext{B}} = 6 imes 1 = 6 cr
& { ext{After 12 years}} cr
& { ext{A}} = 5 + 12 = 17 cr
& { ext{B}} = 6 + 12 = 18 cr
& frac{{ ext{A}}}{{ ext{B}}} = frac{{17}}{{18}} cr} $$
[#263] A person divided Rs. 10800 among his three sons in the ratio 3 : 4 : 5. Second son kept Rs. 1000 for himself, gave Rs. 600 to his wife and divided the remaining money among his two daughters in the ratio 11 : 9. Then one of his daughters received.
Correct Answer
(C) Rs. 1100
Explanation
Solution: $$eqalign{
& { ext{Second son's share}} cr
& = { ext{Rs}}{ ext{.}}left( {10800 imes frac{4}{{12}}}
ight) cr
& = { ext{Rs}}{ ext{. }}3600 cr} $$ Money distributed between the two daughters = Rs. [3600 - (1000 + 600)] = Rs. 2000 $$eqalign{
& { ext{First daughter's share}} cr
& = { ext{Rs}}{ ext{.}}left( {2000 imes frac{{11}}{{20}}}
ight) cr
& = { ext{Rs}}.1100. cr
& { ext{Second daughter's share}} cr
& = { ext{Rs}}{ ext{.}}left( {2000 imes frac{9}{{20}}}
ight) cr
& = { ext{Rs}}{ ext{. 9}}00 cr} $$
[#264] The numbers x, y, z are proportional to 2, 3, 5. The sum of x, y, z is 100. If y = px - 10, then p is equal to.
Correct Answer
(B) 2
Explanation
Solution: $$eqalign{
& o x:y:z = 2:3:5 cr
& herefore x = left( {100 imes frac{2}{{10}}}
ight) = 20 cr
& y = left( {100 imes frac{3}{{10}}}
ight) = 30 cr
& y = px - 10 cr
& Rightarrow 30 = 20p - 10 cr
& Rightarrow 20p = 40 cr
& Rightarrow p = 2 cr} $$
[#265] Of three positive numbers, the ratio of first and second is 8 : 9, that of second and third is 3 : 4. The product of first and third is 2400. The sum of the three number is = ?
Correct Answer
(A) 145
Explanation
Solution: $$eqalign{
& { ext{First}}:{ ext{Second}}:{ ext{Third}} cr
& ,,,,8,,,,,,:,,,,,,9 cr
& ,,,,,,,,,,,,,,,,,,,,,,,3,,,,,,,,,,,:,,,,,4 cr
& frac{{overline {,,24,,,:,,,,,27,,,,,,,,:,,,,36} }}{{underline {,8,,,,,,,,:,,,,,,,,9,,,,,,,,:,,,,12} }} cr
& { ext{Let 8x}}:{ ext{9x}}:{ ext{12x}} cr
& herefore { ext{First}} imes { ext{Third}} cr
& 8x imes 12x = 2400 cr
& Rightarrow 96{x^2} = 2400 cr
& Rightarrow {x^2} = frac{{2400}}{{96}} = 25 cr
& Rightarrow x = 5 cr
& herefore { ext{Sum of three numbers }} cr
& { ext{First}} + { ext{Second}} + { ext{Third}} cr
& 8x + 9x + 12x = 29x cr
& herefore 29 imes 5 = 145 cr} $$