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⁞ Ratio And Proportion

Aptitude ➤ Ratio And Proportion ➤ 1
Question 11
Q11.  What must be added to each of the four members 10, 18, 22, 38 so that they become in proportion ?
 

Answer :  2


Let the number to be added to each of the four members be x.
By the given condition, we get

(10+x) : (18+x) :: (22+x) : (38+x)
⇒ (10+x)(38+x) = (18+x)(22+x)
⇒ 380 + 48x + x2 = 396 + 40x + x2

Cancelling x2 from both sides, we get

380 + 48x = 396 + 40x
⇒ 48x - 40x = 396 - 380
⇒ 8x = 16
⇒ x = 2
⚔ DISCUSS

Question 12
Q12.  In a mixture of 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is:
 

Answer :  60 litres


Quantity of milk = 60 x (2/3) litres = 40 litres.
Quantity of water in it = (60- 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres.
Then, milk : water = 40 : (20+x)

.Now, 40/(20+x) = 1/2
⇒ 20 + x = 80
⇒ x = 60.
∴ Quantity of water to be added = 60 litres.
⚔ DISCUSS

Question 13
Q13.  Tea worth Rs. 126 per Kg and Rs. 135 per Kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per Kg, then the price of the third variety per Kg is
 

Answer :  Rs. 175.50


Let the third type of tea is priced at Rs. x per Kg .

Also , suppose that the three types of tea mixed together are 1, 1 and 2 Kg respectively.

Now,

126×1 + 135×1 + 2x = 153
1 + 1 + 2
261 + 2x = 153
4

⇒ 261 + 2x = 612
x = 351/2 = Rs. 175.50 per Kg


⚔ DISCUSS
Question 14
Q14.  A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
 

Answer :  Rs. 2000


Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then,
4x - 3x = 1000
⇒ x = 1000.

∶ B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
⚔ DISCUSS

Question 15
Q15.  The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
 

Answer :  30


Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 = 5 x (3/5) : 8 x (3/5) = 3 : 24/5
A : B : C = 2 : 3 : 24/5 = 10 : 15 : 24
∴ B = 98 x (15/49) = 30.
⚔ DISCUSS

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