CUET2025-General Test-25/08/2024

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आज की पोस्ट इसप्रकार है:

Q 2774) In 80 litres mixture of milk and water, the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ? (CUET’s General Test held on 29/05/2024)

Ans: 4 litres.

Solution: As given in the question, total mixture = 80 litres and the ratio of milk and water = 7 : 3. It means in mixture milk = 7/10 x 80 = 56 litres and water = 3/10 x 80 =24 litres.

Suppose, y litres of water is to be added in the mixture to make it in the ration 2 : 1, therefore, 56/24+y = 2/1; 56= 2 (24+y); 56= 48+2y; -2y = 48-56 =-8; -2y= -8; y=4 litres.

(Cross checking: 24+4 =28 is half of 56)

Q 2775) The average og 101 consecutive odd numbers is 303. Find the largest number ? (CUET’s General Test held on 29/05/2024)

Ans: 403

Solution: This question is taken from ‘Arithmetic Progression’. Suppose, first odd number is (2n+1); then, 2nd odd number will be (2n+1)+(2-1)(2)= 2n+3; 3rd odd number will be (2n+1)+(3-1)(2)= 2n+5 and 101th odd number will be (2n+1)+(101-1)(2)= (2n+1) + 200= 2n+201

We know that in Arithmetic Progression Sum S_n=(N/2)(a+L)

Here, N= Total odd numbers; a=first term; L= last term.

S_n =(101/2) (2n+1 + 2n+201) = (101/2) (4n+202) = 101(2n+101)

Now, Average = Sum/N; Sum/101; 303= 101(2n+101)/101; 303 = 2n +101;      -2n=101-303; -2n= -202; n=101

Last term (or largest term) = 2n+201 = 2×101 + 201= 403

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