Ratio - Study Mode

[#251] If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : c is equal to
Correct Answer

(A) 2 : 1

Explanation

Solution: $$eqalign{
&,,,, { ext{ }}a{ ext{ }}:{ ext{ }}b{ ext{ }}:{ ext{ }}c cr
&,,,, { ext{ }}3{ ext{ }}:{ ext{ }}4{ ext{ }}:{ ext{ }}7{ ext{ }} cr
& x08oxed{,,3x:4x:7x,,,,} Rightarrow 14x cr
& herefore a + b + c = 14x cr
& c = 7x cr
& herefore left( {a + b + c}
ight):c cr
& = 14x:7x cr
& = 2:1 cr} $$

[#252] If A and B are in the ratio 3 : 4, and B and C in the ratio 12 : 13, then A and C will be in the ratio
Correct Answer

(B) 9 : 13

Explanation

Solution: $$eqalign{
& {frac{A}{B}} imes {frac{B}{C}} = {frac{3}{4}} imes {frac{{12}}{{13}}} cr
& Or,,frac{A}{C} = frac{{36}}{{52}} = 9:13 cr} $$

[#253] The salaries of A, B and C are in the ratio 1 : 3 : 4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio
Correct Answer

(C) 21 : 66 : 92

Explanation

Solution: Let A's Salary = Rs. 100 Then, B's Salary = Rs. 300 And, C's Salary = Rs. 400 Salary has given in 1 : 3 : 4 ratio Now, 5% increase in A's Salary, A's new Salary = (100 + 5% of 100) = Rs. 105 B's Salary increases by 10%, Then, B's new Salary = (300 + 10% of 300) = Rs. 330 C's Salary increases by 15%, C's new Salary = (400 + 15% of 400) = Rs. 460 Then, ratio of increased Salary, A : B : C = 105 : 330 : 460 = 21 : 66 : 92 Alternative 100 (A's salary) === 5%↑ ===> 105(A's increased salary) 300 (B's salary) === 10%↑ ===> 330 (B's increased salary) 400 (C's salary) === 15%↑ ===> 460 (C's increased salary) Ratio of their increased salary = 105 : 330 : 460 = 21 : 66 : 92

[#254] If A : B = 2 : 3 and B : C = 4 : 5 then A : B : C is
Correct Answer

(C) 8 : 12 : 15

Explanation

Solution: $$eqalign{
& frac{{ ext{A}}}{{ ext{B}}} = frac{2}{3} cr
& frac{{ ext{B}}}{{ ext{C}}} = frac{4}{5} cr} $$ A : B : C = 2 × 4 : 3 × 4 : 3 × 5 = 8 : 12 : 15

[#255] In a school having roll strength 286, the ratio of boys and girls is 8 : 5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes
Correct Answer

(D) 4 : 3

Explanation

Solution: Boys : girls = 8 : 5 (let the boys = 8x, girl = 5x) Total strength = 286 8x + 5x = 286 13x = 286 Or, x = $$frac{{286}}{{13}}$$ = 22 Boys = 176 and girls = 110 22 more girls get admitted then number of girls become (5x + 22) = 110 + 22 = 132 Now, new ratio of boys and girls = 176 : 132 = 4 : 3