CAT Questions

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It is Blackboard or Chalkboard which is Black when clean, and as you write on it with white chalk it becomes dirty in White color.

By trial and error method, when we substitute 

x = 0

Both LHS and RHS are equal.

Given that Rs. 1860 will become Rs. 2641.20 at 12%

=> Simple Interest = 2641.20 - 1860 = Rs. 781.20

We know I = PTR/100

=> 781.20 x 100 = 1860 x T x 12

=> T = 78120/1860x12

=> T = 78120/22320

=> T = 3.5 years.

Let the speed of the boat upstream be p kmph and that of downstream be q kmph

Time for upstream = 8 hrs 48 min = 845hrs

Time for downstream = 4 hrs

Distance in both the cases is same.

=> p x  845= q x 4

=> 44p/5 = 4q

=> q = 11p/5

 Now, the required ratio of Speed of boat : Speed of water current

= q+p2:q-p2

=> (11p/5 + p)/2  : (11p/5 - p)/2

=> 8 : 3

The light from the sun takes about 8 minutes to reach the Earth after it has been emitted from the sun's surface.

The time it takes for light to reach planets in our Solar System varies from about 3 minutes for Mercury to about 5.3 hours for Pluto.

Protect the consumer from the seller who cheat to sell his product.

The FTC’s Bureau of Consumer Protection stops unfair, deceptive and fraudulent business practices by collecting complaints and conducting investigations, suing companies and people that break the law, developing rules to maintain a fair marketplace, and educating consumers and businesses about their rights and responsibilities.

Let Karan’s present age be x years and Shiva’s present age be y years.
Then, according to the first condition,
x - 10 = 3(y - 10) or x - 3y = - 20 ..(1)
Now, Karan’s age after 10 years = (x + 10) years
Shiva’s age after 10 years = (y + 10)
(x + 10) = 2 (y + 10) or x - 2y = 10 ..(2)
Solving (1) and (2), we get x = 70 and y = 30
Karan’s age = 70 years and Shiva’s age = 30 years.

The figure may be labelled as shown

Rectangles :

The simplest rectangles are CVSR, VETS, RSWM and STKW i.e 4 in number.

The rectangles composed of two components each are CETR, VEKW, RTKM and CVWM i.e 4 in number.

The rectangles composed of three components each are ACRP, PRMO, EGHT and THIK i.e 4 in number.

The rectangles composed of four components each are CEKM, AVSP, PSWO,VGHS and SHIW i.e 5 in number.

The rectangles composed of five components each are AETP, PTKO, CGHR and RHIM i.e 4 in number.

The rectangles composed of six components each are ACMO and EGIK i.e 2 in number.

The rectangles composed of eight components each are AGHP, PHIO, AVWO and VGIW i.e 4 in number.

The rectangles composed of ten components each are AEKO and CGIM i.e 2 in number.

AGIO is the only rectangle having sixteen components

Total number of rectangles in the given figure = 4 + 4 + 4 + 5 + 4 + 2 + 4 + 2 + 1 = 30.

Hexagons :

The hexagons in the given figure are CDEKLM, CEUKMQ, CFHJMQ, BEUKNP and BFHJNP. So, there are 5 hexagons in the given figure.