Question

What is the ratio of the production of Pulses to that of Wheat over the six years ?

• A. 25 : 27
• B. 23 : 25
• C. 23 : 28
• D. 23 : 27

Hint:

When finding ratios across years, always sum totals before simplifying.

Answer 1

The Correct Option is D

Step 1: Pulses production over years 2011 = 150, 2012 = 50, 2013 = 200, 2014 = 150, 2015 = 250, 2016 = 350. 
Total Pulses = \( 1150 \). 

Step 2: Wheat production over years 2011 = 250, 2012 = 150, 2013 = 400, 2014 = 100, 2015 = 150, 2016 = 300. 
Total Wheat = \( 1350 \). 

Step 3: Ratio Pulses : Wheat = \( 1150 : 1350 = 115 : 135 = 23 : 27 \). \[ \boxed{23 : 27} \] So the correct option is (d)

Answer 2

Instead of dividing by 10 and then by 5 in two steps, the ratio can be reduced in one step by finding the greatest common divisor through prime factorisation.

Totals over the six years. Pulses: \(150+50+200+150+250+350=1150\). Wheat: \(250+150+400+100+150+300=1350\).

Reducing via prime factors. \(1150=2\times5^2\times23\) and \(1350=2\times3^3\times5^2\). The common factors are \(2\times5^2=50\). Dividing both by \(50\): \[ \frac{1150}{50}=23,\qquad \frac{1350}{50}=27. \] So the ratio is \(23:27\).

1. Option 25:27: Would need Pulses total to be \(1250\), not the computed \(1150\); ruled out.
2. Option 23:25: Would need Wheat total to be \(1250\), not the computed \(1350\); ruled out.
3. Option 23:28: Close, but \(1350/50=27\), not 28; ruled out.
4. Option 23:27: Matches exactly, from dividing both totals by their GCD of 50.

Factoring both totals shows their greatest common divisor directly, without needing an intermediate simplification step.

So the correct answer is 23:27.