Ratio - Study Mode

[#191] The fourth proportional to 10, 12, 15 is:
Correct Answer

(C) 18

Explanation

Solution: 10 : 12 :: 15 : a 12 × 15 = 10 × a a = 18

[#192] Alloy A contains copper and zinc in the ratio of 4 : 3 and alloy B contains copper and zinc in the ratio of 5 : 2. A and B are taken in the ratio of 5 : 6 and melted to form a new alloy. The percentage of zinc in the new alloy is closest to:
Correct Answer

(D) 35

Explanation

Solution: [x08egin{array}{*{20}{c}}
{{ ext{Copper}}}&{}&{{ ext{Zinc}}}&{} \
4&:&3&{ Rightarrow {7_{ imes 5}}} \
5&:&2&{ Rightarrow {7_{ imes 6}}}
end{array}] [x08egin{array}{*{20}{c}}
{{ ext{Copper}},,,,,{ ext{Zinc}}} \
{20,,,,,:,,,,,15} \
{30,,,,,:,,,,,12} \
{overline {,50,,,,,:,,,,,27,} }
end{array}] $${ ext{Zinc }}\% = frac{{27}}{{77}} imes 100 = 35\% $$

[#193] One cup has juice and water in the ratio 5 : 2, while another cup of the same capacity has them in the ratio 7 : 4, respectively. If contents of both the cups (when full) are poured in a vessel, then what will be the final ratio of water to juice in the vessel?
Correct Answer

(B) 25 : 52

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{{ ext{Juice}}}&:&{{ ext{Water}}}&{{ ext{Total}}} \
{{{ ext{I}}^{{ ext{st}}}}}&{{5_{ imes 11}}}&:&{{2_{ imes 11}}}&{{7_{ imes 11}}} \
{{ ext{I}}{{ ext{I}}^{{ ext{nd}}}}}&{{7_{ imes 7}}}&:&{{4_{ imes 7}}}&{{{11}_{ imes 7}}}
end{array}] Capacity of both cup is same [x08egin{array}{*{20}{c}}
{}&{{ ext{Juice :}},{ ext{Water}},,,{ ext{Total}}} \
{{{ ext{I}}^{{ ext{st}}}}}&{55,,,:,,,22,,,,,,,,,,77} \
{{ ext{I}}{{ ext{I}}^{{ ext{nd}}}}}&{49,,,:,,,28,,,,,,,,,,77} \
{{ ext{Total}}}&{overline {underline {,104,,:,,50,,,,,,,,,154,} } }
end{array}] Final ratio of water to juice in cup = 50 : 104 = 25 : 52

[#194] A box contains 280 coins of one rupee, 50 paise and 25 paise. The value of each kind of the coins are in the ratio of 8 : 4 : 3. Then the number of 50 paise coins is
Correct Answer

(C) 80

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{{ ext{Rs}}{ ext{. 1}}}&:&{50,{ ext{Paise}}}&:&{25{ ext{ Paise}}} \
{{ ext{Value of coins}}}&{8x}&:&{4x}&:&{3x} \
{{ ext{Number of coins}}}&{8x imes 1}&:&{4x imes 2}&:&{3x imes 4} \
{}&{8x}&:&{8x}&:&{12x}
end{array}] ∴ Total coins ⇒ 8x + 8x + 12x = 28x 28x = 280 xa0 (Given) x = [frac{{280}}{{28}}] = 10 ∴ Number of 50 paise coins are = 8x = 8 × 10 = 80

[#195] In a school, $$frac{3}{8}$$ of the number of students are girls and the rest the are boys. One third of the number of boys are below 10 years and $$frac{2}{3}$$ of the number of girls also below 10 years. If the number of students of age 10 or more years is 260, then the number of boys in the school is:
Correct Answer

(C) 300

Explanation

Solution: Let total students = 72 units 39 units → 260 1 unit → $$frac{{20}}{3}$$ 45 units → $$45 imes frac{{20}}{3}$$ Boys = 300