model 3 fraction of numbers Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

0.121212 .... = 0.$\ov{12}$ = $12/99 = 4/33$

Answer: (d)

$1/15 + 1/35 + 1/63 + 1/99 + 1/143$

= $1/{3×5}+1/{5×7}+1/{7×9}+1/{9×11}+1/{11×13} $

=$1/2(1/3 - 1/5+1/5 - 1/7+1/7 - 1/9+1/9 - 1/11+1/11 - 1/13)$

=$1/2(1/3 - 1/13)$

= $1/2({13 - 3}/39) = 5/39$

Answer: (c)

Let the value of estate be Rs.x

According to the question

$4/5$ of x = 16800

x = ${16800 × 5}/4$ = Rs.21000

$3/7$ of the value = 21000 × $3/7$ = 3000 × 3 = Rs.9000

Answer: (a)

Let the tin contain x bottles of oil.

As given,

$4/5x – 6 + 4 = 3/4x$

$4/5x – 3/4 x$ = 2

$({16 – 15}/20)x$ = 2

$x/20$ = 2 ⇒ x = 2 × 20 = 40

The tin can contain 40 bottles.

Answer: (c)

$6/{7/8} = {6×8}/7 = 48/7$

= ${6/7}/8 = 6/{7×8} = 3/28$

Required difference = $48/7 – 3/28$

= ${192 - 3}/28 = 189/28 = 27/4 = 6{3}/4$

Answer: (d)

Let the length of the rod be x metres.

According to the question,

$x – (x/10 + x/20 + x/30 + x/40 + x/50 + x/60)$ =12.08

$x[1 – ({60 +30 + 20 + 15 + 12 + 10}/600)]$ = 12.08

$x(1 - {147}/600)$ = 12.08

$x({600 - 147}/600)$ = 12.08

$x × 453/600$ = 12.08

$x = {12.08×600}/453$ =16 m.