Practice Basic concepts of ratio and proportion - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) The mean proportional between $(3 +√2)$ and $(12 - √32)$ is
(a)
(b)
(c)
(d)
Using Rule 14Mean Proportion - Let x be the mean proportion between a and b, then a:x::x:b (Real condition)$a/x = x/b ⇒ x^2 =ab$$x =√{ab}$So, mean proportion of a and b = $√{ab}$If x be the mean proportion between (x - a) and (x - b) then what will be the value of x ?$x = {ab}/{a+b}$
Mean proportional
=$√{(3+√2)(12-√{32})}$
= $√{(3+√2)4(3-√2)}$
= 2$√{9 - 2} = 2√7$
Q-2) If a : b : c = 2 : 3 : 4 and 2a - 3b + 4c = 33, then the value of c is
(a)
(b)
(c)
(d)
a : b : c = 2 : 3 : 4
$a/2 = b/3 =c/4$ = k (let)
a = 2k, b = 3k, and c = 4k
Given 2a - 3b + 4c = 33
2 × 2k - 3×3k + 4 ×4k = 33
4k - 9k + 16k = 33
11k = 33 ⇒ k = $33/11$ = 3
c = 4k = 4×3 = 12
Q-3) 94 is divided into two parts in such a way that the fifth part of the first and the eighth part of the second are in the ratio 3 : 4. The first part is :
(a)
(b)
(c)
(d)
First part = x and second part
= 94 - x
${x/5}/{{94 - x}/8} = 3/4$
$x/5 × 8/(94 - x) =3/4$
32 x = 15 × 94 - 15x
47 x = 15 × 94
$x = {15 × 94}/47$ = 30
Q-4) The fourth proportional to 0.12, 0.21, 8 is :
(a)
(b)
(c)
(d)
Let the fourth proportional be x
Then, ${0.12}/{0.21} = 8/x$
or $x =8 ×{0.21}/{0.12}$
or $x =8 × 21/12$
or x = 14
Using Rule 16Fourth Proportional - Let x be the fourth proportional of a, b and c, then a:b::c:x (Real condition)$a/b=c/x ⇒ ax=bc$$x={bc}/a$Fourth proportional of a, b and c =${bc}/a$
Fourth proportion = ${bc}/a$
= ${0.21 ×18}/{0.12}$= 14
Q-5) If p : q : r = 1 : 2 : 4, then $√{5p^2+q^2+r^2}$ is equal to
(a)
(b)
(c)
(d)
$p/1 = q/2 = r/4$ = k (let)
p = k, q = 2k, r = 4k
$√{5p^2 + q^2 + r^2}$
= $√{5k^2 + 4k^2 + 16k^2}$
= $√{25k^2}$ =5k = 5p
Q-6) The ratio of A to B is 4 : 5 and that of B to C is 2 : 3. If A equals 800, C equals
(a)
(b)
(c)
(d)
A : B = 4 : 5
B : C = 2 : 3
A : B : C = 4 × 2 : 5 × 2 : 5 × 3
= 8 : 10 : 15
If A equals 800, then C equals 1500.
Q-7) If a : b = c : d = e : f = 1 : 2, then ( 3a + 5c +7e): (3b + 5d + 7 f ) is equal to
(a)
(b)
(c)
(d)
$a/b = c/d = e/f = 1/2$
${3a}/{3b} = {5c}/{5d} = {7e}/{7f} = 1/2$
${3a+ 5c+7e}/{3b +5d +7f} = 1/2$ = 1 : 2
Q-8) If p : q = r : s = t : u = 2 : 3, then (mp + nr + ot) : (mq + ns + ou) is equal to :
(a)
(b)
(c)
(d)
Using Rule 33If $a/b=c/d=e/f=...,$then each ratio =${a+c+e+...}/{b+d+f+...}$
If $a/b = c/d = e/f$, then each of these ratios is equal to ${a+c+e}/{b+d+ f}$
Here, $p/q =r/s= t/u = 2/3$
${mp}/{mq}= {nr}/{ns}= {ot}/{ou} = 2/3$
${mp +nr+ ot}/{mq+ ns+ ou}= 2/3$ or 2 : 3
Q-9) If x : y = 2 : 3, then the value of ${3x+ 2y}/{9x+ 5y}$ is equal to
(a)
(b)
(c)
(d)
Given, $x/y = 2/3$ ... (i)
Expression = ${3x + 2y}/{9x + 5y}$
= ${3x/y + 2}/{9x/y+ 5} = {3×2/3+2}/{9×2/3+5}$[from (i)]
= ${2 + 2}/11 =4/11$
Q-10) If a, b, c are three numbers such that a : b = 3 : 4 and b : c = 8 : 9, then a : c is equal to
(a)
(b)
(c)
(d)
We can write a : c by compounding a : b and b : c
$a/c = a/b × b/c, a/c = 3/4 × 8/9, a/c =2/3$
a : c = 2 : 3
Using Rule 18If A:B = x:y and B:C = p:q then(i) A:C = xp : yq(ii) A:B:C = (x:y) × p:qy =xp:yp:qy It is done as follows:A:B = x:y B:C = p:qA:B:C = xp:yp:qy
A : C = xp : yq
= 3 × 8 : 4 × 9 = 2 : 3