Question

The sides of a rectangular piece of paper is 2:3. If the area is 150 sq.cm, find the length of its sides.

An alloy consists of 30% copper and 40% zinc, and the remaining is nickel. Find the amount of nickel in 20 kg of alloy.

Which is a better investment? - Rs. 5600 for 8 yrs at 6% or 5000 for 10 yrs at the rate of 5%

Answer 1

1. Let length be 2x
 breadth be 3x
Area= l*b=2x*3x=6x^2
Given area= 150 cm^2
According to the problem, equation is
6x^2=150
x^2=150/6
x^2=25
x=√25
x=5
therefore, length =2x=2*5=10 cm
             breadth=3x=3*5=15cm
2. in the alloy, copper and zinc together are of 70%
  therefore, nickel will be of 30%
so the amount of nickel in 20kg of alloy= 30/100 of 20 = (30 x 20)/100 =6kg
Therefore, the amount of nickel = 6 kg
3. RS.5600 for 8 years at 6% per annum is.
   5600*6/100*8=56*6*8=2688 rs.
 RS. 5000 for 10 years at 5% per annum is
  5000*5/100*10=50*5* 10=2500 Rs.
Therefore, Rs.5600 for 8 yeras at 6% per annum is the best investment.

Answer 2

1.Let the length  of the sides of the rectangular paper be 2x and 3x cm .
Area=2x*3x=6x² cm²
Given,6x² cm² =150 cm²
=>x²=25
=>x=√25
=>x=5
Therefore, the length of its sides are  2x= 2 cm*5=10 cm and 3x=3 cm*5=15 cm respectively.
2.Percentage of copper=30%
Percentage of zinc=40%
Percentage of nickel=%(100-30-40)=30%
Ratio of copper,zinc and nickel in the alloy=30%:40%:30%
=3:4:3
Let the quantity of each metal in 20 kg alloy be 3x , 4x and 3x respectively.
By the condition,
3x+4x+3x=20 kg
=>10x=20 kg
=>x=2 kg
Therefore,Amount of nickel in 20 kg alloy=3x=3*2 kg=6 kg.
3.SI on the first investment=Rs.P*R*T/100
=Rs.5600*6*8/100
=Rs.56*6*8
=Rs.2688
SI on the second investment=Rs.P*R*T/100
=Rs.5000*10*5/100
=Rs.2,500
Therefore,The first investment is better.