Answer:
Speed are 8 km/hr and 15 km/hr
So it takes 15t times and 8t times
Difference of times = 15t ā 8t = 7t
7t = 35 minutes (10:15 min ā 9:40 min)
t = 5 minutes
He takes 75 minutes by travelling at 8 km/hr and 40 minutes if travelled at 15 km/hr
He starts at 9 am.
So, 9:10 to 10:00 = 50 minutes
15 km/hr = 40 min
And at what speed he should travel, so as to reach there within 50 minutes
The answer is, "12"
CAT 2020 Quant Question: Digits
If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is
A. 56
B. 49
C. 46
D. 59
Answer:
Since the product is involved, we will keep the numbers as close as possible
bc = 96 and c < 9
b c
12 Ć 8 = 96
16 Ć 6 = 96
24 Ć 4 = 96
ab = 432
a b
12 Ć 36 = 432
16 Ć 27 = 432
24 Ć 18 = 432
So possible values of a = 36, b = 12, c = 8 Sum = 58
a = 27, b = 16, c = 6 Sum = 49
a = 18, b = 24, c = 4 Sum = 46
Least possible value = 46
Hence, the answer is, "46"
CAT 2020 Quant Question: Exponents & Powers
If y is a negative number such that 
then y equals
Answer:
Hence, the answer is, "log2 (1/3)"
CAT 2020 Quant Question: Mensuration
Q. 22. On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches opposite two sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is
CAT 2020 Quant Question: Percentages
Q. 23. In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to
A. 59
B. 62
C. 66
D. 55
Answer:
In a group 28% are young, 72% are old
In the same group 65% are literates and 35% are illiterates
Young literates = 
(65%) = 16.25%, So remaining 11.75% are young illiterates
Out of 35% illiterates = 11.75% is young and remaining 23.25% are old illiterates
So, 
Ć 100 ā
66
The answer is, "66"
CAT 2020 Quant Question: Mixtures
Q. 24. An alloy is prepared by mixing metals A, B, C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of metals A, B, C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, of the metal C is
A. 84
B. 48
C. 96
D. 70
Answer:
A : B : C
3 : 4 : 7 (Volume)
5 : 2 : 6 (1L of each)
15 : 8 : 42 (Total)
Totally 65kg
Asked in 130 kg Cās weightage
In 65 kg Cās weight = 42kg, So in 130kg Cās weightage = 84kg
The answer is, "84"
CAT 2020 Quant Question: Sequence ā§ Series
Q. 25. A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?
Answer:
Let us take 5th kid has 2 toffees
Because we know that after 5th toffee his stock exhausts.
So only if the 5th kid has 2 toffees, he can give away half of it and 1 extra = 0
Then for 4th kid, (2+1) Ć 2 = 6 (Since we are moving in reversing order)
3rd = 14 and 2nd = 30 and 1st kid = 62
The answer is, " 62"
CAT 2020 Quant Question: Ratio & Proportions
Q. 26. A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3?
Answer:
40 litres is split in ratio 2:3
So dye = 16 l and water = 24 l
Now proportion is 2:5
Already in the ratios 2:3
2 : 5
Now, 16 l of dye : 40 l of water
16 l of water is added
is removed from the proportion
12 l of dye : 30 l of water
Now how many dye has to be added to make 2 : 3
2 : 3
12 l of dye : 30 l of water
Multiplication factor is 10 (3 Ć 10 = 30)
2 Ć 10 = 20 l of dye in total,
So 8 l of dye has to be added
The answer is, "8"
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CAT 2020Quant Question: Races
In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is
A. 550
B. 475
C. 500
D. 450
Answer:
Let the length of the race track be āxā km.
By the time A finishes the race, B lags by 45km.
That is, in the same time, while A runs x kms, B runs (x-45) kms
Ratio of Speeds of A and B = 
By the time B finishes the race, C lags by 50km.
That is, in the same time, while B runs x kms, C runs (x-50) kms
Ratio of Speeds of B and C = 
By the time A finishes the race, C lags by 90km.
That is, in the same time, while A runs x kms, C runs (x-90) kms
Ratio of Speeds of A and C = 
(Ratio of Speeds of A and B) Ć (Ratio of Speeds of B and C) = (Ratio of Speeds of A and C)
9x = 10x - 450
x = 450.
OR
Ratio of Speeds of A and B = 
By the A covers x, B covers 0.9x
Since A beats B by 45km, 0.1x = 45
x = 450.
Hence, the answer is, "450"
CAT 2020 Quant Question: Geometry
From the interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the perpendiculars is āsā. Then the area of the triangle is
