Ratio - Study Mode
[#161] In an innings of a cricket match,three players A, B and C scored a total of 361 runs. If the ratio of the number of runs scored by A to that scored by B and also number of runs scored by B to that scored by C be 3 : 2, the number of runs scored by A was = ?
Correct Answer
(A) 171
Explanation
Solution: Given total runs of A, B, C (A + B + C = 361) $$eqalign{
& Rightarrow { ext{A}}:{ ext{B}}:{ ext{C}} cr
& ,,,,,,,,,3:2 cr
& ,,,,,,,,,,,,,,,,,3:2 cr
& underline {overline {,,,,,,,,,,9:6:4{ ext{ }}} } cr
& herefore 9x + 6x + 4x = 361 cr
& Rightarrow 19x = 361 cr
& Rightarrow x = 19 cr
& herefore { ext{Runs scored by A }} cr
& = 9x cr
& = 9 imes 19 cr
& = 171 cr} $$
[#162] If A : B = 2 : 3, B : C = 4 : 5 and C : D = 5 : 9 then A : D is equal to:
Correct Answer
(B) 8 : 27
Explanation
Solution: $$eqalign{
& frac{A}{D} = {frac{A}{B}} imes {frac{B}{C}} imes {frac{C}{D}} cr
& ,,,,,,,,, = {frac{2}{3}} imes {frac{4}{5}} imes {frac{5}{9}} cr
& ,,,,,,,,, = frac{{ {2 imes 4 imes 5} }}{{ {3 imes 5 imes 9} }} cr
& ,,,,,,,,, = frac{8}{{27}} cr
& ,,,,,,,,, = 8:27 cr} $$
[#163] In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is
Correct Answer
(B) 3 : 4
Explanation
Solution: Girls : boys = 6 : 5
Hence, girls = $$6 imes frac{{66}}{{11}}$$ xa0= 36 Boys = 30 New ratio, 30 : (36 + 4) = 3 : 4
[#164] What must be added to each term of the ratio 7 : 11, So as to make it equal to 3 : 4?
Correct Answer
(D) 5
Explanation
Solution: $$eqalign{
& { ext{Let }}x{ ext{ be added to each term}}. cr
& { ext{According to question}}, cr
& frac{{ {7 + x} }}{{11 + x}} = frac{3}{4} cr
& Or,,33 + 3x = 28 + 4x cr
& Or,,x = 5 cr} $$
[#165] Two numbers are in ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. The smaller number is
Correct Answer
(B) 49
Explanation
Solution: Let the numbers be 7x and 11x. $$eqalign{
& { ext{According to question}}, cr
& frac{{ {7x + 7} }}{{ {11x + 7} }} = frac{2}{3} cr
& Or,,22x + 14 = 21x + 21 cr
& Or,,x = 7 cr
& { ext{Smaller}},{ ext{number}} = 49 cr} $$