Question

In December 2014, Bala spent 75% of his income on food, shopping and utility bills. The amounts that he spent on food, shopping and utility bills is 7 : 6 : 2. In February 2015, Bala spent 72% of his income on food, shopping and utility bills. The amount that he spent on food, shopping and utility bills is 22 : 19 : 7. The amount he spent on utility bills in February 2015 was 16 2./3 % more than that in December 2014. The percentage by which his income in December 2014 was less than that in February 2015 is

Answer 1

Solution :-

Let us assume that, In December 2014, Bala income was Rs.100x .

so,

→ Bala spent on food, shopping and utility bills = 75% of 100x = Rs.75x .

then,

→ Amount spent on food = (7/15) * 75x = Rs.35x

→ Amount spent on shopping = (6/15) * 75x = Rs.30x

→ Amount spent on utility bills = (2/15) * 75x = Rs.10x

Now, Let us assume that, In February 2015, Bala income was Rs.100y .

so,

→ Bala spent on food, shopping and utility bills = 72% of 100y = Rs.72y .

then,

→ Amount spent on food = (22/48) * 72y = Rs.33y

→ Amount spent on shopping = (19/48) * 72y = Rs.28.5y

→ Amount spent on utility bills = (7/48) * 72y = Rs.10.5y

now, given that, The amount he spent on utility bills in February 2015 was 16 2./3 % more than that in December 2014.

therefore,

→ 10.5y = 116(2/3)[10x]

→ 10.5y = (350/3) * 10x

→ 10.5y * 3 = 3500x

→ 31.5y = 3500x

→ y/x = (35000/315)

→ y/x = (7000/63)

→ y/x = (1000/9)

hence,

→ Income in December 2014 = 100x = 100*9 = Rs.9000

→ Income in February 2015 = 100y = 100 * 1000 = Rs.100000

∴

→ Less income in December 2014 = 100000 - 9000 = Rs.91000

→ % Less income than In february 2015 = (91000 * 100) / 100000 = 91% (Ans.)

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