makefile not finding header file from -I include path

I have the makefile given below. When I do make I get the following error

cc  -c -o timing.o timing.c
test_c.c:5:17: fatal error: test.h: No such file or directory
 #include "test.h"

I have manually verfied that test.h is present in ../include path. I am not sure why this is not finding the header file.It would be great if someone could help.Also I would expect g++ instead of cc

# Makefile template for shared library

CXX = g++ # C++ compiler                                                                                                                                                                     
CXXFLAGS = -fPIC -Wall -Wextra -O2 -g -I../include #CXX flags
LDFLAGS = -lboost_system -shared  # linking flags

RM = rm -f  # rm command

TARGET_LIB = libtest.a # target lib


C_SRCS := test_a.c test_b.c 
CPP_SRCS := test_c.cpp test_d.cpp 
OBJS := $(C_SRCS:.c=.o) $(CPP_SRCS:.cpp=.o)

.PHONY: all 

all: ${TARGET_LIB}

$(TARGET_LIB): $(OBJS) 
    $(CXX) $(CXXFLAGS) ${LDFLAGS} -o $@ $^  


.PHONY: clean
clean:
    -${RM} ${TARGET_LIB} ${OBJS} 

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