GATE Questions

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Given total number of cows = k
Now, 1st son share = k/2
2nd son share = k/4
3rd son share = k/5
4th son share = 9

(k) + (k/4) + (k/5) + 9 = k
=> k - (19k/20) = 9
=> (20k-19k)/20 = 9
=> k = 180.

Ratio of investments of A, B & C =>

Share of C = 1530

Share of B = 765

Share of A = 1020

Given rate of wheat at cheap = Rs. 2.90/kg

Rate of wheat at cost = Rs. 3.20/kg

Mixture rate = Rs. 3/kg

Ratio of mixture = 

          2.90                              3.20

                              3

(3.20 - 3 = 0.20)            (3 - 2.90 = 0.10)

0.20 : 0.10 = 2:1

Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.

Let Anushka age = X
Charu latha 12 yrs older than Anushka so Charu latha age = x+12
Kajal is thrice as old as Anushka so Kajal age = 3x
The ages of Anushka, Kajal and Charu latha together are 57 years
i.e x + (x+12) + 3x = 57
=> 5x = 45
:- x = 9
Anushka age = 9
Kajal age = 3x = 27
Charu latha age = x+12 = 21

(16M + 12W) x 20 = 18W x 40

=> 2M = 3W

Then,
Convert all men into women

12M + 27W = 27 + 12 x 3/2W = 45W

Let number of days required be 'D'

=> 18 x 40 = 45 x D

=> D = 16 days.

Here the given words, sullen and moody are synonyms to each other which means that gloomy, resentful. Similarly, repetitious and monotonous are synonyms to each other which means dull, tedious.

Hence, Sullen : moody :: monotonous : repetitious.

Let the length be 'l' and breadth be 'b'.

b = l × 3/4__________(a)

2(l+b) = 1050

l+b = 525___________(b)

From equations (a) and (b),

l = 300m, b = 225 m

Area = l × b

= 300 × 225

= 67500 sq.m.

Since  Area of Rectangle = side1 x side2
Therefore, error% in area
= x + y + xy100 %
= [20 - 10 + ( -10 x 20)/100]% or 8%
i.e. 8% excess.