type 1 basic concepts of ratio & proportion Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

a : b = c : d

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

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

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

Answer: (a)

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

Answer: (a)

A : B = $1/2 : 3/8$ =4 : 3 = 8 : 6

B : C = $1/3 : 5/9$ = 3 : 5 = 6 : 10

C : D = $5/6 : 3/4$ = 10 : 9

A : B : C : D = 8 : 6 : 10 : 9

Answer: (d)

Ratio = $1/2 : 1/3 : 1/5$

= $1/2 × 30 : 1/3 × 30 : 1/5$ × 30

= 15 : 10 : 6

Sum of the ratios

= 15 + 10 + 6 = 31

First part

= Rs.$15/31$ × 6200 = Rs.3000

Second part

= Rs.$10/31$ × 6200 = Rs.2000

Third part

= Rs.$6/31$ × 6200 = Rs.1200

Answer: (a)

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