type 1 basic concepts of ratio & proportion Practice Questions Answers Test with Solutions & More Shortcuts

Question : 6 [SSC CGL Prelim 2007]

If a : b = c : d, then ${ma+ nc}/{mb +nd}$ is not equal to

a) ${a +c}/{b +d}$

b) ${c - a}/{b - d}$

c) $c/d$

d) $a/b$

Answer: (a)

a : b = c : d

$a/b = c/d = {ma}/{mb} = {nc}/{nd}$

${a + c}/{b + d} = {ma + nc}/{mb + nd}$

Question : 7 [SSC CHSL 2012]

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) 40

b) 28

c) 36

d) 30

Answer: (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

Question : 8 [SSC CGL Prelim 2000]

If p : q = r : s = t : u = 2 : 3, then (mp + nr + ot) : (mq + ns + ou) is equal to :

a) 2 : 3

b) 3 : 2

c) 1 : 2

d) 1 : 3

Answer: (a)

Using Rule 33
If $a/b=c/d=e/f=...,$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

Question : 9 [SSC CGL Prelim 2000]

If m : n = 3 : 2, then (4m + 5n) : (4m - 5n) is equal to :

a) 11 : 1

b) 9 : 1

c) 9 : 4

d) 4 : 9

Answer: (a)

$m/n = 3/2$ (Given)

${4m+ 5n}/{4m- 5n}={4(m/n)+ 5}/{4(m/n)- 5}$

= ${4 ×3/2 +5}/{4× 3/2- 5}={6 +5}/{6- 5}$ = 11: 1

Question : 10 [SSC CGL Prelim 2005]

If a : b = 5 : 7 and c : d = 2a : 3b, then ac : bd is :

a) 10 : 21

b) 50 : 151

c) 50 : 147

d) 20 : 38

Answer: (c)

$a/b = 5/7, c/d = {2a}/{3b}$

$a/b ×c/d= 5/7 ×{2a}/{3b}$

${ac}/{bd} = 10/21× 5/7 = 50/147$

= 50 : 147

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