AMCAT Equations Quiz-1

Answer: 48
Explanation:
x = 16 , Y = 8
(x+y)x/y = (16+8)*16/8
= 48

Answer: 160
Explanation:
Let the current ages of idols of Lord Shiva and Krishna be 25x, and 18x,
After 10 years, their ages will be 25x+10 and 18x+10

Given,
25x+10 / 18x+10 = 7 / 5
=> 125x + 50 = 126x + 70
=> x = 20
Hence, their present ages are
Lord Shiva =15x= 300 years;
Lord Krishna =8x = 160 years

Answer: 4
Solution
(3z + 4) = 2(z+3 +23)
3z + 4 = 2z +6 + 46
3z -2z = 6 +46 -4
z = 4

Answer: 45
Solution
Let Ravendra has number of pen = x
Let Amrinder has number of pen = y
x+y = 60--------(1)
x = 3y -----------(2)
Put value of x = 2y in equation 1
3y + y = 60
4y = 60
y = 15
x = 60 -15 = 45
Ravendra has 45 pens

Correct Option: Two
Let the maximum marks in each subject be 100.

∴ Gautam Gambhir’s total score = 70% of (100 + 100 + 100) = 0.7(300) = 210
Also, 80% marks in a subject correspond to 0.8(100) = 80
Let Gautam’s have scored 4x, 5x and 6x in the three subjects.
∴ x + 3x + 3x = 210
∴ 7x = 210
x = 30
Hence, his marks in the three subjects are 30, 90 and 90 .
Hence, he has scored more than 80 in exactly two subjects.

Answer: 1200
Solution:
Let the length of the train be l.
Then the distance covered by the train in 1 minute is equal to the length of the train.
Speed of train = 54 km/hr = (72 × 1000) / 60 m/min = 1200 m/min
But, x/1 = 1200
⇒ x = 1200 × 1 = 1200 m
∴ the length of the train is 1200 m.

Correct Option: 3/2
Given equations,
3x + 4y = 5 ........ (i)
x + 2y = 2 .........(ii)
Solving (i) and (ii), we get
y = (1 / 2) and x = 1. so x + y = 3 / 2

Correct Option: 11
Let a two-digit number be (10x + y) and reversing number be (10y + x)
∴ Required sum = 10x + y + 10y + x = 11x + 11y = 11(x + y)
Hence, it's divisible by 11.

Correct Option: 66
Let the greater number be x and smaller number be y
∴ x – y = 44 ..... (i)
and x = 5y ..... (ii)
From eqs. (i) and (ii)
5y – y = 44
⇒ y = 44 / 4 = 11
On putting the value of y in Eq. (ii), we get
x = 11 * 5 = 55
Hence, required sum = x + y = 55 + 11 = 66.

Answer: 17
Explanation:
Let there be 1 kg cake.
1 kg = 1000 g
Father ate 1/5th of the cake.
⇒ 1000*1/5
= 200 g
So, the father ate 200 g of cake.
Remaining quantity of cake = 1000 - 200 = 800 g
Let the number of members in the family excluding father be x
Father had 4 times as much as others had. So, each family member will get = 200/4
Therefore, number of family members = x*(200/4) = 800
⇒ 200x = 800*4
⇒ 200x = 3200
⇒ x = 3200/200
⇒ x = 16
Total members in the family = 16 + 1 father
= 17 member