type 5 shares & partnership based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Suppose amount received by men = 5x.

and amount received by women = 4x

According to question

5x + 4x = 180

9x = 180 ⇒ x = 20

Amount received by men = Rs.100

Amount received by women= Rs.80

Suppose the number of men be y and that of women be (66 - y).

According to question

${100/y}/{80/{66 - y}} = 3/2$

$100/y × {66 - y}/80 = 3/2$

${5(66 - y)}/{4y} = 3/2$

660 - 10y = 12y

22y = 660 ⇒ y = 30

Answer: (a)

$2/5A + 40 = 2/7B + 20$

= $9/17 C + 10 = x$

A = $5/2(x - 40)$, B = $7/2(x - 20)$

and, C = $17/9(x -10)$

$5/2(x - 40) + 7/2(x - 20) + 17/9(x -10)$ = 600

x = 100

A’s share

= Rs.$5/2$(100 - 40) = Rs.150

Answer: (c)

A : B = 2 : 3 = 8 : 12

B : C = 4 : 5 = 12 : 15

A : B : C = 8 : 12 : 15

Sum of ratios = 35

A’s share = $8/35 × 700$ = Rs.160

B’s share = $12/35 × 700$ = Rs.240

C’s share = $15/35 × 700$ = Rs.300

Answer: (b)

Let the amount to be distributed be Rs.x.

P : Q : R = 2 : 7 : 9

Sum of the ratios = 2+7 + 9 = 18

P = $2/18 × x = x/9$

Q = $7/18$ x

R = ${9x}/18 = x/2$

As given,

$x/9 + {7x}/18 = x/2$

Thus, we get no conclusion.

Amount should necessarily be known.

Answer: (d)

Son : wife = 3 : 1 = 9 : 3

Wife : daughter = 3 : 1

Son : wife : daughter

= 9 : 3 : 1

Sum of ratios = 9 + 3 + 1 = 13

If total wealth be Rs.x, then

Son’s share - daughter’s share

= Rs.10,000

${9x}/13 - x/13$ = 10,000

${9x - x}/13$ = 10,000

8x = 13,00,00

$x = {13,00,00}/8$ = Rs.16250

Answer: (b)

Original ratio of A, B and C

= $1/2 : 1/3 : 1/4$ = 6 : 4 : 3

Share of A

= $6/13 × 117$ = Rs.54

Share of B

= $4/13 × 117$ = Rs.36

and share of C

= $3/13 × 117$ = Rs.27

The ratio of A, B and C by mistake = 2 : 3 : 4

Share of A = $2/9 × 117$ = Rs.26

Share of B = $3/9 × 117$ = Rs.39

Share of C = $4/9 × 117$ = Rs.52

Therefore, it is clear from above calculation that C gains maximum i.e. Rs.25.