Ratio, Proportion & Partnership: (part 2 )Exercise Problem & solved examples

Question: 10 Given (P + 7Q)/4P = 19/20, what is the ratio of Q:P?
Option: (a) 1:2 (b) 1:3 (c) 2:4 (d) 2:5 (e) 2:7

Explore: (P + 7Q)/4P = 19/20
=> 20P + 140Q = 76P
=> 140Q = 56P
=> P/Q = 140/56 = 5/2
=> P:Q = 5:2
:. Q:P = 2:5

Answer: (d)

Question: 11 Nine years ago the age of P and Q| were in the ratio of 2:3. After 7 years, the ratio of their age will be 3:4. What is the present age of P?

Explore: Let 9 years ago the age of P and Q were 2x & 3x respectively.
:. Present age of P = 2x + 9 
Present age of Q = 3x + 9
According to the question,
(2x +9+7):(3x+9+7) = 3:4
=> (2x+16)/(3x+16) = 3/4
=> 4(2x+16) = 3(3x +16)
=> 8x + 64 = 9x +48
=> 9x-8x = 64 - 48
=> x = 16
:. Present age of P = 2 x 16 + 9 = 41
Answer: 41

Question: 12 Age of three persons are now in the proportion 2:3:4 and in 5 years from now, the proportion will be 5:7:8. What is the present age of the youngest person?
Option: (a) 30 (b) 25 (c) 20 (d) 15 (e) None

Explore: The ratio of the age of the three persons is 2:3:4. So, their age can be 2X, 3X, 4X, where X is any number.
After 5 years their age ratio is given by 5:7:8. So, their age may be 5Y, 7Y & 8Y where Y is any other number.
So, we can write
2X+5 = 5Y .......(1)
3X+5 = 7Y .......(2)

(2) - (1) gives X = 2Y
Or, Y = 1/2
Replacing this value in (1)
2X +5 = (5/2)X
Or, 5 = ((5/2) - 2)X = (1/2)X
:. X = 10
:. Required age 2X = 2x10 = 20
Answer: (c)

Question: 13 A fruit salad mixture consists of apples, peaches and grapes in the ratio 6:5:2 respectively, by weights. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

Explore: In the mixture of 39 pounds,
ratio of apples, peaches & grapes = 6:5:2
:. Weight of apples = 39 x (6/(6+5+2)) = 39 x (6/13) = 18 Pounds
Weight of peaches = 39 x (5/13) = 15 Pounds
Weight of grapes = 39 x (2/13) = 6 Pounds
:. Weight of apples is (18 - 6) or 12 pounds more than grapes.
Answer: 12 pounds

Question: 14 Jahirul and Jalil agree to form a partnership. The partnership agreement requires that Jahirul invest $7,000 less than one half of what Jalil invests. If the total investment is $ 1,25,000 how much does Jalil invest?

Explore: Let, Jalil invest $X
:. Jahirul invests $ (X/2) - 7000
According to the question,
X+(X/2) - 7000 = 125000
=> (2X+X)/2 = 125000+7000
=> 3X/2 = 132000
:. X = (132000 x 2)/3
=> X = 88000
Answer: Jalil invests $ 88000

Question: 15 Arif, Babu and Salm started a business jointly with a total amount of $28000. Arif paid $ 4500 more than Babu and Babu paid $7000 less than Salam. If the company made a profit of $5600, how much profit should Babu receive?

Explore: Let Babu paid $X
:. Arif paid $(X+4500)
Salam paid $(X+7000)
According to the question,
X+X+4500+X+7000 = 2800
=> 3X + 11500 = 28000
=> 3X = 28000 - 11500
=> X = (16500/3) = 5500
:. Babu paid $ 5500
Arif paid $ (5500+4500) = $10000
Salam paid $ (5500 + 7000) = $12500
They will share profit according to the money they paid.
:. Ratio of money paid by Babu, Arif and Salam
= 5500:10000:12500
= 55:100:125
= 11:20:25
Some of the ratio = 11+20+25 = 56
:. Babu received from the profit of $5600
= $5600 x (11/56)
= $1100
Answer: $1100

Question: 16 Arif, Babu and Salam started a business jointly with a total amount of $280. Arif paid $45 more than Babu and Babu paid $70 less than Salam. If the company made a profit of $56, how much profit should Babu receive?
Option: (a) 22 (b) 20 (c) 25 (d) 27 (e) None

Explore: Let, Babu's investment be $B
:. Arif's investment is $(B+45)
And Salam's investment $ (B+70)
According to the problem,
b+(b+45)+(b+70) = 280
=> 3B = 280 -115 = 165
:. B = 55
Since the profit is shared in proportion of capital investment, so,
Babu's profit = ((Babu's capital)/(Total capital)) x Total profit = ((55)/(250)) x 56 = $11
Answer: (e)

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